KILLED
proof of input_AmUhda8kyk.trs
# AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished


The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF).

(0) CpxTRS
(1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(2) CpxTRS
(3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
(4) CpxTRS
(5) CpxTrsToCdtProof [UPPER BOUND(ID), 44 ms]
(6) CdtProblem
    (7) CdtToCpxRelTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (8) CpxRelTRS
    (9) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (10) CpxRelTRS
        (11) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
        (12) typed CpxTrs
        (13) OrderProof [LOWER BOUND(ID), 5 ms]
        (14) typed CpxTrs
        (15) RewriteLemmaProof [LOWER BOUND(ID), 592 ms]
        (16) typed CpxTrs
        (17) RewriteLemmaProof [LOWER BOUND(ID), 4028 ms]
        (18) typed CpxTrs
        (19) RewriteLemmaProof [LOWER BOUND(ID), 2046 ms]
        (20) typed CpxTrs
    (21) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
    (22) TRS for Loop Detection
(23) RelTrsToWeightedTrsProof [UPPER BOUND(ID), 0 ms]
(24) CpxWeightedTrs
    (25) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (26) CpxTypedWeightedTrs
    (27) CompletionProof [UPPER BOUND(ID), 0 ms]
    (28) CpxTypedWeightedCompleteTrs
        (29) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
        (30) CpxRNTS
    (31) CompletionProof [UPPER BOUND(ID), 0 ms]
    (32) CpxTypedWeightedCompleteTrs
        (33) NarrowingProof [BOTH BOUNDS(ID, ID), 189 ms]
        (34) CpxTypedWeightedCompleteTrs
        (35) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 8 ms]
        (36) CpxRNTS
        (37) InliningProof [UPPER BOUND(ID), 693 ms]
        (38) CpxRNTS
        (39) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (40) CpxRNTS
(41) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms]
(42) CdtProblem
    (43) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (44) CdtProblem
    (45) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (46) CdtProblem
    (47) CdtToCpxRelTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (48) CpxRelTRS
        (49) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
        (50) CpxTRS
        (51) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
        (52) CpxWeightedTrs
            (53) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
            (54) CpxTypedWeightedTrs
            (55) CompletionProof [UPPER BOUND(ID), 6 ms]
            (56) CpxTypedWeightedCompleteTrs
            (57) CompletionProof [UPPER BOUND(ID), 45 ms]
            (58) CpxTypedWeightedCompleteTrs
                (59) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
                (60) CpxRNTS
    (61) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (62) CdtProblem
        (63) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (64) CdtProblem
        (65) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (66) CdtProblem
        (67) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (68) CdtProblem
        (69) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (70) CdtProblem
        (71) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (72) CdtProblem
        (73) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (74) CdtProblem
        (75) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (76) CdtProblem
        (77) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (78) CdtProblem
        (79) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (80) CdtProblem
        (81) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 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), 15 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), 14 ms]
        (98) CdtProblem
        (99) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (100) CdtProblem
        (101) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (102) CdtProblem
        (103) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (104) CdtProblem
        (105) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (106) CdtProblem
        (107) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (108) CdtProblem
        (109) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (110) CdtProblem
        (111) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (112) CdtProblem
        (113) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (114) CdtProblem
        (115) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (116) CdtProblem
        (117) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 31 ms]
        (118) CdtProblem
        (119) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (120) CdtProblem
        (121) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 14 ms]
        (122) CdtProblem
        (123) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (124) CdtProblem
        (125) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (126) CdtProblem
        (127) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 44 ms]
        (128) CdtProblem
        (129) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (130) CdtProblem
        (131) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (132) CdtProblem
        (133) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 89 ms]
        (134) CdtProblem
        (135) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (136) CdtProblem
        (137) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 65 ms]
        (138) CdtProblem
        (139) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (140) CdtProblem
        (141) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 9 ms]
        (142) CdtProblem
        (143) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 33 ms]
        (144) CdtProblem
        (145) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 12 ms]
        (146) CdtProblem
        (147) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (148) CdtProblem
        (149) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (150) CdtProblem
        (151) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (152) CdtProblem
        (153) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 6 ms]
        (154) CdtProblem
        (155) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (156) CdtProblem
        (157) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 21 ms]
        (158) CdtProblem
        (159) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (160) CdtProblem
        (161) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (162) CdtProblem
        (163) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (164) CdtProblem
        (165) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 19 ms]
        (166) CdtProblem
        (167) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (168) CdtProblem
        (169) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 14 ms]
        (170) CdtProblem
        (171) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (172) CdtProblem
        (173) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 13 ms]
        (174) CdtProblem
        (175) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 22 ms]
        (176) CdtProblem
        (177) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (178) CdtProblem
        (179) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 4 ms]
        (180) CdtProblem
        (181) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (182) CdtProblem
        (183) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 21 ms]
        (184) CdtProblem
        (185) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (186) CdtProblem
        (187) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 34 ms]
        (188) CdtProblem
        (189) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (190) CdtProblem
        (191) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 12 ms]
        (192) CdtProblem
        (193) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 16 ms]
        (194) CdtProblem
        (195) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 12 ms]
        (196) CdtProblem
        (197) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 53 ms]
        (198) CdtProblem
        (199) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 10 ms]
        (200) CdtProblem
        (201) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 7 ms]
        (202) CdtProblem
        (203) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (204) CdtProblem
        (205) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 21 ms]
        (206) CdtProblem
        (207) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (208) CdtProblem
        (209) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2 ms]
        (210) CdtProblem
        (211) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 4 ms]
        (212) CdtProblem
        (213) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 25 ms]
        (214) CdtProblem
        (215) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (216) CdtProblem
        (217) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 5 ms]
        (218) CdtProblem
        (219) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (220) CdtProblem
        (221) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 15 ms]
        (222) CdtProblem
        (223) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (224) CdtProblem
        (225) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (226) CdtProblem
        (227) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 35 ms]
        (228) CdtProblem
        (229) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 10 ms]
        (230) CdtProblem
        (231) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 39 ms]
        (232) CdtProblem
        (233) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 6 ms]
        (234) 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__and(tt, T) -> mark(T)
   a__isNatIList(IL) -> a__isNatList(IL)
   a__isNat(0) -> tt
   a__isNat(s(N)) -> a__isNat(N)
   a__isNat(length(L)) -> a__isNatList(L)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(N, IL)) -> a__and(a__isNat(N), a__isNatIList(IL))
   a__isNatList(nil) -> tt
   a__isNatList(cons(N, L)) -> a__and(a__isNat(N), a__isNatList(L))
   a__isNatList(take(N, IL)) -> a__and(a__isNat(N), a__isNatIList(IL))
   a__zeros -> cons(0, zeros)
   a__take(0, IL) -> a__uTake1(a__isNatIList(IL))
   a__uTake1(tt) -> nil
   a__take(s(M), cons(N, IL)) -> a__uTake2(a__and(a__isNat(M), a__and(a__isNat(N), a__isNatIList(IL))), M, N, IL)
   a__uTake2(tt, M, N, IL) -> cons(mark(N), take(M, IL))
   a__length(cons(N, L)) -> a__uLength(a__and(a__isNat(N), a__isNatList(L)), L)
   a__uLength(tt, L) -> s(a__length(mark(L)))
   mark(and(X1, X2)) -> a__and(mark(X1), mark(X2))
   mark(isNatIList(X)) -> a__isNatIList(X)
   mark(isNatList(X)) -> a__isNatList(X)
   mark(isNat(X)) -> a__isNat(X)
   mark(length(X)) -> a__length(mark(X))
   mark(zeros) -> a__zeros
   mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
   mark(uTake1(X)) -> a__uTake1(mark(X))
   mark(uTake2(X1, X2, X3, X4)) -> a__uTake2(mark(X1), X2, X3, X4)
   mark(uLength(X1, X2)) -> a__uLength(mark(X1), X2)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(X)) -> s(mark(X))
   mark(cons(X1, X2)) -> cons(mark(X1), X2)
   mark(nil) -> nil
   a__and(X1, X2) -> and(X1, X2)
   a__isNatIList(X) -> isNatIList(X)
   a__isNatList(X) -> isNatList(X)
   a__isNat(X) -> isNat(X)
   a__length(X) -> length(X)
   a__zeros -> zeros
   a__take(X1, X2) -> take(X1, X2)
   a__uTake1(X) -> uTake1(X)
   a__uTake2(X1, X2, X3, X4) -> uTake2(X1, X2, X3, X4)
   a__uLength(X1, X2) -> uLength(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__and(tt, T) -> mark(T)
   a__isNatIList(IL) -> a__isNatList(IL)
   a__isNat(0') -> tt
   a__isNat(s(N)) -> a__isNat(N)
   a__isNat(length(L)) -> a__isNatList(L)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(N, IL)) -> a__and(a__isNat(N), a__isNatIList(IL))
   a__isNatList(nil) -> tt
   a__isNatList(cons(N, L)) -> a__and(a__isNat(N), a__isNatList(L))
   a__isNatList(take(N, IL)) -> a__and(a__isNat(N), a__isNatIList(IL))
   a__zeros -> cons(0', zeros)
   a__take(0', IL) -> a__uTake1(a__isNatIList(IL))
   a__uTake1(tt) -> nil
   a__take(s(M), cons(N, IL)) -> a__uTake2(a__and(a__isNat(M), a__and(a__isNat(N), a__isNatIList(IL))), M, N, IL)
   a__uTake2(tt, M, N, IL) -> cons(mark(N), take(M, IL))
   a__length(cons(N, L)) -> a__uLength(a__and(a__isNat(N), a__isNatList(L)), L)
   a__uLength(tt, L) -> s(a__length(mark(L)))
   mark(and(X1, X2)) -> a__and(mark(X1), mark(X2))
   mark(isNatIList(X)) -> a__isNatIList(X)
   mark(isNatList(X)) -> a__isNatList(X)
   mark(isNat(X)) -> a__isNat(X)
   mark(length(X)) -> a__length(mark(X))
   mark(zeros) -> a__zeros
   mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
   mark(uTake1(X)) -> a__uTake1(mark(X))
   mark(uTake2(X1, X2, X3, X4)) -> a__uTake2(mark(X1), X2, X3, X4)
   mark(uLength(X1, X2)) -> a__uLength(mark(X1), X2)
   mark(tt) -> tt
   mark(0') -> 0'
   mark(s(X)) -> s(mark(X))
   mark(cons(X1, X2)) -> cons(mark(X1), X2)
   mark(nil) -> nil
   a__and(X1, X2) -> and(X1, X2)
   a__isNatIList(X) -> isNatIList(X)
   a__isNatList(X) -> isNatList(X)
   a__isNat(X) -> isNat(X)
   a__length(X) -> length(X)
   a__zeros -> zeros
   a__take(X1, X2) -> take(X1, X2)
   a__uTake1(X) -> uTake1(X)
   a__uTake2(X1, X2, X3, X4) -> uTake2(X1, X2, X3, X4)
   a__uLength(X1, X2) -> uLength(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__and(tt, T) -> mark(T)
   a__isNatIList(IL) -> a__isNatList(IL)
   a__isNat(0) -> tt
   a__isNat(s(N)) -> a__isNat(N)
   a__isNat(length(L)) -> a__isNatList(L)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(N, IL)) -> a__and(a__isNat(N), a__isNatIList(IL))
   a__isNatList(nil) -> tt
   a__isNatList(cons(N, L)) -> a__and(a__isNat(N), a__isNatList(L))
   a__isNatList(take(N, IL)) -> a__and(a__isNat(N), a__isNatIList(IL))
   a__zeros -> cons(0, zeros)
   a__take(0, IL) -> a__uTake1(a__isNatIList(IL))
   a__uTake1(tt) -> nil
   a__take(s(M), cons(N, IL)) -> a__uTake2(a__and(a__isNat(M), a__and(a__isNat(N), a__isNatIList(IL))), M, N, IL)
   a__uTake2(tt, M, N, IL) -> cons(mark(N), take(M, IL))
   a__length(cons(N, L)) -> a__uLength(a__and(a__isNat(N), a__isNatList(L)), L)
   a__uLength(tt, L) -> s(a__length(mark(L)))
   mark(and(X1, X2)) -> a__and(mark(X1), mark(X2))
   mark(isNatIList(X)) -> a__isNatIList(X)
   mark(isNatList(X)) -> a__isNatList(X)
   mark(isNat(X)) -> a__isNat(X)
   mark(length(X)) -> a__length(mark(X))
   mark(zeros) -> a__zeros
   mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
   mark(uTake1(X)) -> a__uTake1(mark(X))
   mark(uTake2(X1, X2, X3, X4)) -> a__uTake2(mark(X1), X2, X3, X4)
   mark(uLength(X1, X2)) -> a__uLength(mark(X1), X2)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(X)) -> s(mark(X))
   mark(cons(X1, X2)) -> cons(mark(X1), X2)
   mark(nil) -> nil
   a__and(X1, X2) -> and(X1, X2)
   a__isNatIList(X) -> isNatIList(X)
   a__isNatList(X) -> isNatList(X)
   a__isNat(X) -> isNat(X)
   a__length(X) -> length(X)
   a__zeros -> zeros
   a__take(X1, X2) -> take(X1, X2)
   a__uTake1(X) -> uTake1(X)
   a__uTake2(X1, X2, X3, X4) -> uTake2(X1, X2, X3, X4)
   a__uLength(X1, X2) -> uLength(X1, X2)

S is empty.
Rewrite Strategy: PARALLEL_INNERMOST
----------------------------------------

(5) CpxTrsToCdtProof (UPPER BOUND(ID))
Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT
----------------------------------------

(6)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__AND(z0, z1) -> c1
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNATILIST(zeros) -> c3
   A__ISNATILIST(cons(z0, z1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNAT(z0))
   A__ISNATILIST(cons(z0, z1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNATILIST(z1))
   A__ISNATILIST(z0) -> c6
   A__ISNAT(0) -> c7
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__ISNAT(z0) -> c10
   A__ISNATLIST(nil) -> c11
   A__ISNATLIST(cons(z0, z1)) -> c12(A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
   A__ISNATLIST(cons(z0, z1)) -> c13(A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__ISNATLIST(take(z0, z1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNAT(z0))
   A__ISNATLIST(take(z0, z1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNATILIST(z1))
   A__ISNATLIST(z0) -> c16
   A__ZEROS -> c17
   A__ZEROS -> c18
   A__TAKE(0, z0) -> c19(A__UTAKE1(a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(z0), cons(z1, z2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__ISNAT(z0))
   A__TAKE(s(z0), cons(z1, z2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNAT(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNATILIST(z2))
   A__TAKE(z0, z1) -> c23
   A__UTAKE1(tt) -> c24
   A__UTAKE1(z0) -> c25
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   A__UTAKE2(z0, z1, z2, z3) -> c27
   A__LENGTH(cons(z0, z1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
   A__LENGTH(cons(z0, z1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__LENGTH(z0) -> c30
   A__ULENGTH(tt, z0) -> c31(A__LENGTH(mark(z0)), MARK(z0))
   A__ULENGTH(z0, z1) -> c32
   MARK(and(z0, z1)) -> c33(A__AND(mark(z0), mark(z1)), MARK(z0))
   MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
   MARK(zeros) -> c39(A__ZEROS)
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake1(z0)) -> c42(A__UTAKE1(mark(z0)), MARK(z0))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(tt) -> c45
   MARK(0) -> c46
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   MARK(nil) -> c49
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__AND(z0, z1) -> c1
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNATILIST(zeros) -> c3
   A__ISNATILIST(cons(z0, z1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNAT(z0))
   A__ISNATILIST(cons(z0, z1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNATILIST(z1))
   A__ISNATILIST(z0) -> c6
   A__ISNAT(0) -> c7
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__ISNAT(z0) -> c10
   A__ISNATLIST(nil) -> c11
   A__ISNATLIST(cons(z0, z1)) -> c12(A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
   A__ISNATLIST(cons(z0, z1)) -> c13(A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__ISNATLIST(take(z0, z1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNAT(z0))
   A__ISNATLIST(take(z0, z1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNATILIST(z1))
   A__ISNATLIST(z0) -> c16
   A__ZEROS -> c17
   A__ZEROS -> c18
   A__TAKE(0, z0) -> c19(A__UTAKE1(a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(z0), cons(z1, z2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__ISNAT(z0))
   A__TAKE(s(z0), cons(z1, z2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNAT(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNATILIST(z2))
   A__TAKE(z0, z1) -> c23
   A__UTAKE1(tt) -> c24
   A__UTAKE1(z0) -> c25
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   A__UTAKE2(z0, z1, z2, z3) -> c27
   A__LENGTH(cons(z0, z1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
   A__LENGTH(cons(z0, z1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__LENGTH(z0) -> c30
   A__ULENGTH(tt, z0) -> c31(A__LENGTH(mark(z0)), MARK(z0))
   A__ULENGTH(z0, z1) -> c32
   MARK(and(z0, z1)) -> c33(A__AND(mark(z0), mark(z1)), MARK(z0))
   MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
   MARK(zeros) -> c39(A__ZEROS)
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake1(z0)) -> c42(A__UTAKE1(mark(z0)), MARK(z0))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(tt) -> c45
   MARK(0) -> c46
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   MARK(nil) -> c49
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__ISNATLIST_1, A__ZEROS, A__TAKE_2, A__UTAKE1_1, A__UTAKE2_4, A__LENGTH_1, A__ULENGTH_2, MARK_1

Compound Symbols:   c_1, c1, c2_1, c3, c4_2, c5_2, c6, c7, c8_1, c9_1, c10, c11, c12_2, c13_2, c14_2, c15_2, c16, c17, c18, c19_2, c20_3, c21_4, c22_4, c23, c24, c25, c26_1, c27, c28_3, c29_3, c30, c31_2, c32, c33_2, c34_2, c35_1, c36_1, c37_1, c38_2, c39_1, c40_2, c41_2, c42_2, c43_2, c44_2, c45, c46, c47_1, c48_1, c49


----------------------------------------

(7) CdtToCpxRelTrsProof (BOTH BOUNDS(ID, ID))
Converted S to standard rules, and D \ S as well as R to relative rules.
----------------------------------------

(8)
Obligation:
The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF).


The TRS R consists of the following rules:

   A__AND(tt, z0) -> c(MARK(z0))
   A__AND(z0, z1) -> c1
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNATILIST(zeros) -> c3
   A__ISNATILIST(cons(z0, z1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNAT(z0))
   A__ISNATILIST(cons(z0, z1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNATILIST(z1))
   A__ISNATILIST(z0) -> c6
   A__ISNAT(0) -> c7
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__ISNAT(z0) -> c10
   A__ISNATLIST(nil) -> c11
   A__ISNATLIST(cons(z0, z1)) -> c12(A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
   A__ISNATLIST(cons(z0, z1)) -> c13(A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__ISNATLIST(take(z0, z1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNAT(z0))
   A__ISNATLIST(take(z0, z1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNATILIST(z1))
   A__ISNATLIST(z0) -> c16
   A__ZEROS -> c17
   A__ZEROS -> c18
   A__TAKE(0, z0) -> c19(A__UTAKE1(a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(z0), cons(z1, z2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__ISNAT(z0))
   A__TAKE(s(z0), cons(z1, z2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNAT(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNATILIST(z2))
   A__TAKE(z0, z1) -> c23
   A__UTAKE1(tt) -> c24
   A__UTAKE1(z0) -> c25
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   A__UTAKE2(z0, z1, z2, z3) -> c27
   A__LENGTH(cons(z0, z1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
   A__LENGTH(cons(z0, z1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__LENGTH(z0) -> c30
   A__ULENGTH(tt, z0) -> c31(A__LENGTH(mark(z0)), MARK(z0))
   A__ULENGTH(z0, z1) -> c32
   MARK(and(z0, z1)) -> c33(A__AND(mark(z0), mark(z1)), MARK(z0))
   MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
   MARK(zeros) -> c39(A__ZEROS)
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake1(z0)) -> c42(A__UTAKE1(mark(z0)), MARK(z0))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(tt) -> c45
   MARK(0) -> c46
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   MARK(nil) -> c49

The (relative) TRS S consists of the following rules:

   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil

Rewrite Strategy: INNERMOST
----------------------------------------

(9) RenamingProof (BOTH BOUNDS(ID, ID))
Renamed function symbols to avoid clashes with predefined symbol.
----------------------------------------

(10)
Obligation:
The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF).


The TRS R consists of the following rules:

   A__AND(tt, z0) -> c(MARK(z0))
   A__AND(z0, z1) -> c1
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNATILIST(zeros) -> c3
   A__ISNATILIST(cons(z0, z1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNAT(z0))
   A__ISNATILIST(cons(z0, z1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNATILIST(z1))
   A__ISNATILIST(z0) -> c6
   A__ISNAT(0') -> c7
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__ISNAT(z0) -> c10
   A__ISNATLIST(nil) -> c11
   A__ISNATLIST(cons(z0, z1)) -> c12(A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
   A__ISNATLIST(cons(z0, z1)) -> c13(A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__ISNATLIST(take(z0, z1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNAT(z0))
   A__ISNATLIST(take(z0, z1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNATILIST(z1))
   A__ISNATLIST(z0) -> c16
   A__ZEROS -> c17
   A__ZEROS -> c18
   A__TAKE(0', z0) -> c19(A__UTAKE1(a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(z0), cons(z1, z2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__ISNAT(z0))
   A__TAKE(s(z0), cons(z1, z2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNAT(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNATILIST(z2))
   A__TAKE(z0, z1) -> c23
   A__UTAKE1(tt) -> c24
   A__UTAKE1(z0) -> c25
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   A__UTAKE2(z0, z1, z2, z3) -> c27
   A__LENGTH(cons(z0, z1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
   A__LENGTH(cons(z0, z1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__LENGTH(z0) -> c30
   A__ULENGTH(tt, z0) -> c31(A__LENGTH(mark(z0)), MARK(z0))
   A__ULENGTH(z0, z1) -> c32
   MARK(and(z0, z1)) -> c33(A__AND(mark(z0), mark(z1)), MARK(z0))
   MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
   MARK(zeros) -> c39(A__ZEROS)
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake1(z0)) -> c42(A__UTAKE1(mark(z0)), MARK(z0))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(tt) -> c45
   MARK(0') -> c46
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   MARK(nil) -> c49

The (relative) TRS S consists of the following rules:

   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0') -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0', zeros)
   a__zeros -> zeros
   a__take(0', z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0') -> 0'
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil

Rewrite Strategy: INNERMOST
----------------------------------------

(11) TypeInferenceProof (BOTH BOUNDS(ID, ID))
Inferred types.
----------------------------------------

(12)
Obligation:
Innermost TRS:
Rules:
A__AND(tt, z0) -> c(MARK(z0))
A__AND(z0, z1) -> c1
A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
A__ISNATILIST(zeros) -> c3
A__ISNATILIST(cons(z0, z1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNAT(z0))
A__ISNATILIST(cons(z0, z1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNATILIST(z1))
A__ISNATILIST(z0) -> c6
A__ISNAT(0') -> c7
A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
A__ISNAT(z0) -> c10
A__ISNATLIST(nil) -> c11
A__ISNATLIST(cons(z0, z1)) -> c12(A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
A__ISNATLIST(cons(z0, z1)) -> c13(A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
A__ISNATLIST(take(z0, z1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNAT(z0))
A__ISNATLIST(take(z0, z1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNATILIST(z1))
A__ISNATLIST(z0) -> c16
A__ZEROS -> c17
A__ZEROS -> c18
A__TAKE(0', z0) -> c19(A__UTAKE1(a__isNatIList(z0)), A__ISNATILIST(z0))
A__TAKE(s(z0), cons(z1, z2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__ISNAT(z0))
A__TAKE(s(z0), cons(z1, z2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNAT(z1))
A__TAKE(s(z0), cons(z1, z2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNATILIST(z2))
A__TAKE(z0, z1) -> c23
A__UTAKE1(tt) -> c24
A__UTAKE1(z0) -> c25
A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
A__UTAKE2(z0, z1, z2, z3) -> c27
A__LENGTH(cons(z0, z1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
A__LENGTH(cons(z0, z1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
A__LENGTH(z0) -> c30
A__ULENGTH(tt, z0) -> c31(A__LENGTH(mark(z0)), MARK(z0))
A__ULENGTH(z0, z1) -> c32
MARK(and(z0, z1)) -> c33(A__AND(mark(z0), mark(z1)), MARK(z0))
MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1))
MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
MARK(isNat(z0)) -> c37(A__ISNAT(z0))
MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
MARK(zeros) -> c39(A__ZEROS)
MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
MARK(uTake1(z0)) -> c42(A__UTAKE1(mark(z0)), MARK(z0))
MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
MARK(tt) -> c45
MARK(0') -> c46
MARK(s(z0)) -> c47(MARK(z0))
MARK(cons(z0, z1)) -> c48(MARK(z0))
MARK(nil) -> c49
a__and(tt, z0) -> mark(z0)
a__and(z0, z1) -> and(z0, z1)
a__isNatIList(z0) -> a__isNatList(z0)
a__isNatIList(zeros) -> tt
a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
a__isNatIList(z0) -> isNatIList(z0)
a__isNat(0') -> tt
a__isNat(s(z0)) -> a__isNat(z0)
a__isNat(length(z0)) -> a__isNatList(z0)
a__isNat(z0) -> isNat(z0)
a__isNatList(nil) -> tt
a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
a__isNatList(z0) -> isNatList(z0)
a__zeros -> cons(0', zeros)
a__zeros -> zeros
a__take(0', z0) -> a__uTake1(a__isNatIList(z0))
a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
a__take(z0, z1) -> take(z0, z1)
a__uTake1(tt) -> nil
a__uTake1(z0) -> uTake1(z0)
a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
a__length(z0) -> length(z0)
a__uLength(tt, z0) -> s(a__length(mark(z0)))
a__uLength(z0, z1) -> uLength(z0, z1)
mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
mark(isNatIList(z0)) -> a__isNatIList(z0)
mark(isNatList(z0)) -> a__isNatList(z0)
mark(isNat(z0)) -> a__isNat(z0)
mark(length(z0)) -> a__length(mark(z0))
mark(zeros) -> a__zeros
mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
mark(uTake1(z0)) -> a__uTake1(mark(z0))
mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
mark(tt) -> tt
mark(0') -> 0'
mark(s(z0)) -> s(mark(z0))
mark(cons(z0, z1)) -> cons(mark(z0), z1)
mark(nil) -> nil

Types:
A__AND :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> c:c1
tt :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c :: c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49 -> c:c1
MARK :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
c1 :: c:c1
A__ISNATILIST :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> c2:c3:c4:c5:c6
c2 :: c11:c12:c13:c14:c15:c16 -> c2:c3:c4:c5:c6
A__ISNATLIST :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> c11:c12:c13:c14:c15:c16
zeros :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c3 :: c2:c3:c4:c5:c6
cons :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c4 :: c:c1 -> c7:c8:c9:c10 -> c2:c3:c4:c5:c6
a__isNat :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
a__isNatIList :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
A__ISNAT :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> c7:c8:c9:c10
c5 :: c:c1 -> c2:c3:c4:c5:c6 -> c2:c3:c4:c5:c6
c6 :: c2:c3:c4:c5:c6
0' :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c7 :: c7:c8:c9:c10
s :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c8 :: c7:c8:c9:c10 -> c7:c8:c9:c10
length :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c9 :: c11:c12:c13:c14:c15:c16 -> c7:c8:c9:c10
c10 :: c7:c8:c9:c10
nil :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c11 :: c11:c12:c13:c14:c15:c16
c12 :: c:c1 -> c7:c8:c9:c10 -> c11:c12:c13:c14:c15:c16
a__isNatList :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c13 :: c:c1 -> c11:c12:c13:c14:c15:c16 -> c11:c12:c13:c14:c15:c16
take :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c14 :: c:c1 -> c7:c8:c9:c10 -> c11:c12:c13:c14:c15:c16
c15 :: c:c1 -> c2:c3:c4:c5:c6 -> c11:c12:c13:c14:c15:c16
c16 :: c11:c12:c13:c14:c15:c16
A__ZEROS :: c17:c18
c17 :: c17:c18
c18 :: c17:c18
A__TAKE :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> c19:c20:c21:c22:c23
c19 :: c24:c25 -> c2:c3:c4:c5:c6 -> c19:c20:c21:c22:c23
A__UTAKE1 :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> c24:c25
c20 :: c26:c27 -> c:c1 -> c7:c8:c9:c10 -> c19:c20:c21:c22:c23
A__UTAKE2 :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> c26:c27
a__and :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c21 :: c26:c27 -> c:c1 -> c:c1 -> c7:c8:c9:c10 -> c19:c20:c21:c22:c23
c22 :: c26:c27 -> c:c1 -> c:c1 -> c2:c3:c4:c5:c6 -> c19:c20:c21:c22:c23
c23 :: c19:c20:c21:c22:c23
c24 :: c24:c25
c25 :: c24:c25
c26 :: c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49 -> c26:c27
c27 :: c26:c27
A__LENGTH :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> c28:c29:c30
c28 :: c31:c32 -> c:c1 -> c7:c8:c9:c10 -> c28:c29:c30
A__ULENGTH :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> c31:c32
c29 :: c31:c32 -> c:c1 -> c11:c12:c13:c14:c15:c16 -> c28:c29:c30
c30 :: c28:c29:c30
c31 :: c28:c29:c30 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49 -> c31:c32
mark :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c32 :: c31:c32
and :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c33 :: c:c1 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
c34 :: c:c1 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
isNatIList :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c35 :: c2:c3:c4:c5:c6 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
isNatList :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c36 :: c11:c12:c13:c14:c15:c16 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
isNat :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c37 :: c7:c8:c9:c10 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
c38 :: c28:c29:c30 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
c39 :: c17:c18 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
c40 :: c19:c20:c21:c22:c23 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
c41 :: c19:c20:c21:c22:c23 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
uTake1 :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c42 :: c24:c25 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
uTake2 :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c43 :: c26:c27 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
uLength :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c44 :: c31:c32 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
c45 :: c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
c46 :: c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
c47 :: c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
c48 :: c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
c49 :: c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
a__zeros :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
a__take :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
a__uTake1 :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
a__uTake2 :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
a__length :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
a__uLength :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
hole_c:c11_50 :: c:c1
hole_tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength2_50 :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
hole_c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c493_50 :: c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
hole_c2:c3:c4:c5:c64_50 :: c2:c3:c4:c5:c6
hole_c11:c12:c13:c14:c15:c165_50 :: c11:c12:c13:c14:c15:c16
hole_c7:c8:c9:c106_50 :: c7:c8:c9:c10
hole_c17:c187_50 :: c17:c18
hole_c19:c20:c21:c22:c238_50 :: c19:c20:c21:c22:c23
hole_c24:c259_50 :: c24:c25
hole_c26:c2710_50 :: c26:c27
hole_c28:c29:c3011_50 :: c28:c29:c30
hole_c31:c3212_50 :: c31:c32
gen_tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength13_50 :: Nat -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
gen_c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c4914_50 :: Nat -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
gen_c2:c3:c4:c5:c615_50 :: Nat -> c2:c3:c4:c5:c6
gen_c11:c12:c13:c14:c15:c1616_50 :: Nat -> c11:c12:c13:c14:c15:c16
gen_c7:c8:c9:c1017_50 :: Nat -> c7:c8:c9:c10

----------------------------------------

(13) OrderProof (LOWER BOUND(ID))
Heuristically decided to analyse the following defined symbols:
A__AND, MARK, A__ISNATILIST, A__ISNATLIST, a__isNat, a__isNatIList, A__ISNAT, a__isNatList, a__and, A__LENGTH, A__ULENGTH, mark, a__length, a__uLength

They will be analysed ascendingly in the following order:
A__AND = MARK
A__AND = A__ISNATILIST
A__AND = A__ISNATLIST
A__AND = A__ISNAT
A__AND = A__LENGTH
A__AND = A__ULENGTH
MARK = A__ISNATILIST
MARK = A__ISNATLIST
a__isNat < MARK
a__isNatIList < MARK
MARK = A__ISNAT
a__and < MARK
MARK = A__LENGTH
MARK = A__ULENGTH
mark < MARK
A__ISNATILIST = A__ISNATLIST
a__isNat < A__ISNATILIST
a__isNatIList < A__ISNATILIST
A__ISNATILIST = A__ISNAT
A__ISNATILIST = A__LENGTH
A__ISNATILIST = A__ULENGTH
a__isNat < A__ISNATLIST
a__isNatIList < A__ISNATLIST
A__ISNATLIST = A__ISNAT
a__isNatList < A__ISNATLIST
A__ISNATLIST = A__LENGTH
A__ISNATLIST = A__ULENGTH
a__isNat = a__isNatIList
a__isNat = a__isNatList
a__isNat = a__and
a__isNat < A__LENGTH
a__isNat = mark
a__isNat = a__length
a__isNat = a__uLength
a__isNatIList = a__isNatList
a__isNatIList = a__and
a__isNatIList = mark
a__isNatIList = a__length
a__isNatIList = a__uLength
A__ISNAT = A__LENGTH
A__ISNAT = A__ULENGTH
a__isNatList = a__and
a__isNatList < A__LENGTH
a__isNatList = mark
a__isNatList = a__length
a__isNatList = a__uLength
a__and < A__LENGTH
a__and = mark
a__and = a__length
a__and = a__uLength
A__LENGTH = A__ULENGTH
mark < A__ULENGTH
mark = a__length
mark = a__uLength
a__length = a__uLength

----------------------------------------

(14)
Obligation:
Innermost TRS:
Rules:
A__AND(tt, z0) -> c(MARK(z0))
A__AND(z0, z1) -> c1
A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
A__ISNATILIST(zeros) -> c3
A__ISNATILIST(cons(z0, z1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNAT(z0))
A__ISNATILIST(cons(z0, z1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNATILIST(z1))
A__ISNATILIST(z0) -> c6
A__ISNAT(0') -> c7
A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
A__ISNAT(z0) -> c10
A__ISNATLIST(nil) -> c11
A__ISNATLIST(cons(z0, z1)) -> c12(A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
A__ISNATLIST(cons(z0, z1)) -> c13(A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
A__ISNATLIST(take(z0, z1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNAT(z0))
A__ISNATLIST(take(z0, z1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNATILIST(z1))
A__ISNATLIST(z0) -> c16
A__ZEROS -> c17
A__ZEROS -> c18
A__TAKE(0', z0) -> c19(A__UTAKE1(a__isNatIList(z0)), A__ISNATILIST(z0))
A__TAKE(s(z0), cons(z1, z2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__ISNAT(z0))
A__TAKE(s(z0), cons(z1, z2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNAT(z1))
A__TAKE(s(z0), cons(z1, z2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNATILIST(z2))
A__TAKE(z0, z1) -> c23
A__UTAKE1(tt) -> c24
A__UTAKE1(z0) -> c25
A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
A__UTAKE2(z0, z1, z2, z3) -> c27
A__LENGTH(cons(z0, z1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
A__LENGTH(cons(z0, z1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
A__LENGTH(z0) -> c30
A__ULENGTH(tt, z0) -> c31(A__LENGTH(mark(z0)), MARK(z0))
A__ULENGTH(z0, z1) -> c32
MARK(and(z0, z1)) -> c33(A__AND(mark(z0), mark(z1)), MARK(z0))
MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1))
MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
MARK(isNat(z0)) -> c37(A__ISNAT(z0))
MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
MARK(zeros) -> c39(A__ZEROS)
MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
MARK(uTake1(z0)) -> c42(A__UTAKE1(mark(z0)), MARK(z0))
MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
MARK(tt) -> c45
MARK(0') -> c46
MARK(s(z0)) -> c47(MARK(z0))
MARK(cons(z0, z1)) -> c48(MARK(z0))
MARK(nil) -> c49
a__and(tt, z0) -> mark(z0)
a__and(z0, z1) -> and(z0, z1)
a__isNatIList(z0) -> a__isNatList(z0)
a__isNatIList(zeros) -> tt
a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
a__isNatIList(z0) -> isNatIList(z0)
a__isNat(0') -> tt
a__isNat(s(z0)) -> a__isNat(z0)
a__isNat(length(z0)) -> a__isNatList(z0)
a__isNat(z0) -> isNat(z0)
a__isNatList(nil) -> tt
a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
a__isNatList(z0) -> isNatList(z0)
a__zeros -> cons(0', zeros)
a__zeros -> zeros
a__take(0', z0) -> a__uTake1(a__isNatIList(z0))
a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
a__take(z0, z1) -> take(z0, z1)
a__uTake1(tt) -> nil
a__uTake1(z0) -> uTake1(z0)
a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
a__length(z0) -> length(z0)
a__uLength(tt, z0) -> s(a__length(mark(z0)))
a__uLength(z0, z1) -> uLength(z0, z1)
mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
mark(isNatIList(z0)) -> a__isNatIList(z0)
mark(isNatList(z0)) -> a__isNatList(z0)
mark(isNat(z0)) -> a__isNat(z0)
mark(length(z0)) -> a__length(mark(z0))
mark(zeros) -> a__zeros
mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
mark(uTake1(z0)) -> a__uTake1(mark(z0))
mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
mark(tt) -> tt
mark(0') -> 0'
mark(s(z0)) -> s(mark(z0))
mark(cons(z0, z1)) -> cons(mark(z0), z1)
mark(nil) -> nil

Types:
A__AND :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> c:c1
tt :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c :: c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49 -> c:c1
MARK :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
c1 :: c:c1
A__ISNATILIST :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> c2:c3:c4:c5:c6
c2 :: c11:c12:c13:c14:c15:c16 -> c2:c3:c4:c5:c6
A__ISNATLIST :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> c11:c12:c13:c14:c15:c16
zeros :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c3 :: c2:c3:c4:c5:c6
cons :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c4 :: c:c1 -> c7:c8:c9:c10 -> c2:c3:c4:c5:c6
a__isNat :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
a__isNatIList :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
A__ISNAT :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> c7:c8:c9:c10
c5 :: c:c1 -> c2:c3:c4:c5:c6 -> c2:c3:c4:c5:c6
c6 :: c2:c3:c4:c5:c6
0' :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c7 :: c7:c8:c9:c10
s :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c8 :: c7:c8:c9:c10 -> c7:c8:c9:c10
length :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c9 :: c11:c12:c13:c14:c15:c16 -> c7:c8:c9:c10
c10 :: c7:c8:c9:c10
nil :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c11 :: c11:c12:c13:c14:c15:c16
c12 :: c:c1 -> c7:c8:c9:c10 -> c11:c12:c13:c14:c15:c16
a__isNatList :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c13 :: c:c1 -> c11:c12:c13:c14:c15:c16 -> c11:c12:c13:c14:c15:c16
take :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c14 :: c:c1 -> c7:c8:c9:c10 -> c11:c12:c13:c14:c15:c16
c15 :: c:c1 -> c2:c3:c4:c5:c6 -> c11:c12:c13:c14:c15:c16
c16 :: c11:c12:c13:c14:c15:c16
A__ZEROS :: c17:c18
c17 :: c17:c18
c18 :: c17:c18
A__TAKE :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> c19:c20:c21:c22:c23
c19 :: c24:c25 -> c2:c3:c4:c5:c6 -> c19:c20:c21:c22:c23
A__UTAKE1 :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> c24:c25
c20 :: c26:c27 -> c:c1 -> c7:c8:c9:c10 -> c19:c20:c21:c22:c23
A__UTAKE2 :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> c26:c27
a__and :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c21 :: c26:c27 -> c:c1 -> c:c1 -> c7:c8:c9:c10 -> c19:c20:c21:c22:c23
c22 :: c26:c27 -> c:c1 -> c:c1 -> c2:c3:c4:c5:c6 -> c19:c20:c21:c22:c23
c23 :: c19:c20:c21:c22:c23
c24 :: c24:c25
c25 :: c24:c25
c26 :: c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49 -> c26:c27
c27 :: c26:c27
A__LENGTH :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> c28:c29:c30
c28 :: c31:c32 -> c:c1 -> c7:c8:c9:c10 -> c28:c29:c30
A__ULENGTH :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> c31:c32
c29 :: c31:c32 -> c:c1 -> c11:c12:c13:c14:c15:c16 -> c28:c29:c30
c30 :: c28:c29:c30
c31 :: c28:c29:c30 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49 -> c31:c32
mark :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c32 :: c31:c32
and :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c33 :: c:c1 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
c34 :: c:c1 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
isNatIList :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c35 :: c2:c3:c4:c5:c6 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
isNatList :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c36 :: c11:c12:c13:c14:c15:c16 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
isNat :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c37 :: c7:c8:c9:c10 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
c38 :: c28:c29:c30 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
c39 :: c17:c18 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
c40 :: c19:c20:c21:c22:c23 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
c41 :: c19:c20:c21:c22:c23 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
uTake1 :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c42 :: c24:c25 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
uTake2 :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c43 :: c26:c27 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
uLength :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c44 :: c31:c32 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
c45 :: c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
c46 :: c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
c47 :: c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
c48 :: c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
c49 :: c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
a__zeros :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
a__take :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
a__uTake1 :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
a__uTake2 :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
a__length :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
a__uLength :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
hole_c:c11_50 :: c:c1
hole_tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength2_50 :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
hole_c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c493_50 :: c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
hole_c2:c3:c4:c5:c64_50 :: c2:c3:c4:c5:c6
hole_c11:c12:c13:c14:c15:c165_50 :: c11:c12:c13:c14:c15:c16
hole_c7:c8:c9:c106_50 :: c7:c8:c9:c10
hole_c17:c187_50 :: c17:c18
hole_c19:c20:c21:c22:c238_50 :: c19:c20:c21:c22:c23
hole_c24:c259_50 :: c24:c25
hole_c26:c2710_50 :: c26:c27
hole_c28:c29:c3011_50 :: c28:c29:c30
hole_c31:c3212_50 :: c31:c32
gen_tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength13_50 :: Nat -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
gen_c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c4914_50 :: Nat -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
gen_c2:c3:c4:c5:c615_50 :: Nat -> c2:c3:c4:c5:c6
gen_c11:c12:c13:c14:c15:c1616_50 :: Nat -> c11:c12:c13:c14:c15:c16
gen_c7:c8:c9:c1017_50 :: Nat -> c7:c8:c9:c10


Generator Equations:
gen_tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength13_50(0) <=> tt
gen_tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength13_50(+(x, 1)) <=> cons(tt, gen_tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength13_50(x))
gen_c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c4914_50(0) <=> c35(c2(c11))
gen_c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c4914_50(+(x, 1)) <=> c33(c(c35(c2(c11))), gen_c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c4914_50(x))
gen_c2:c3:c4:c5:c615_50(0) <=> c2(c11)
gen_c2:c3:c4:c5:c615_50(+(x, 1)) <=> c5(c(c35(c2(c11))), gen_c2:c3:c4:c5:c615_50(x))
gen_c11:c12:c13:c14:c15:c1616_50(0) <=> c11
gen_c11:c12:c13:c14:c15:c1616_50(+(x, 1)) <=> c13(c(c35(c2(c11))), gen_c11:c12:c13:c14:c15:c1616_50(x))
gen_c7:c8:c9:c1017_50(0) <=> c7
gen_c7:c8:c9:c1017_50(+(x, 1)) <=> c8(gen_c7:c8:c9:c1017_50(x))


The following defined symbols remain to be analysed:
a__isNatList, A__AND, MARK, A__ISNATILIST, A__ISNATLIST, a__isNat, a__isNatIList, A__ISNAT, a__and, A__LENGTH, A__ULENGTH, mark, a__length, a__uLength

They will be analysed ascendingly in the following order:
A__AND = MARK
A__AND = A__ISNATILIST
A__AND = A__ISNATLIST
A__AND = A__ISNAT
A__AND = A__LENGTH
A__AND = A__ULENGTH
MARK = A__ISNATILIST
MARK = A__ISNATLIST
a__isNat < MARK
a__isNatIList < MARK
MARK = A__ISNAT
a__and < MARK
MARK = A__LENGTH
MARK = A__ULENGTH
mark < MARK
A__ISNATILIST = A__ISNATLIST
a__isNat < A__ISNATILIST
a__isNatIList < A__ISNATILIST
A__ISNATILIST = A__ISNAT
A__ISNATILIST = A__LENGTH
A__ISNATILIST = A__ULENGTH
a__isNat < A__ISNATLIST
a__isNatIList < A__ISNATLIST
A__ISNATLIST = A__ISNAT
a__isNatList < A__ISNATLIST
A__ISNATLIST = A__LENGTH
A__ISNATLIST = A__ULENGTH
a__isNat = a__isNatIList
a__isNat = a__isNatList
a__isNat = a__and
a__isNat < A__LENGTH
a__isNat = mark
a__isNat = a__length
a__isNat = a__uLength
a__isNatIList = a__isNatList
a__isNatIList = a__and
a__isNatIList = mark
a__isNatIList = a__length
a__isNatIList = a__uLength
A__ISNAT = A__LENGTH
A__ISNAT = A__ULENGTH
a__isNatList = a__and
a__isNatList < A__LENGTH
a__isNatList = mark
a__isNatList = a__length
a__isNatList = a__uLength
a__and < A__LENGTH
a__and = mark
a__and = a__length
a__and = a__uLength
A__LENGTH = A__ULENGTH
mark < A__ULENGTH
mark = a__length
mark = a__uLength
a__length = a__uLength

----------------------------------------

(15) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
a__isNatList(gen_tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength13_50(+(1, n19_50))) -> *18_50, rt in Omega(0)

Induction Base:
a__isNatList(gen_tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength13_50(+(1, 0)))

Induction Step:
a__isNatList(gen_tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength13_50(+(1, +(n19_50, 1)))) ->_R^Omega(0)
a__and(a__isNat(tt), a__isNatList(gen_tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength13_50(+(1, n19_50)))) ->_R^Omega(0)
a__and(isNat(tt), a__isNatList(gen_tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength13_50(+(1, n19_50)))) ->_IH
a__and(isNat(tt), *18_50)

We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0).
----------------------------------------

(16)
Obligation:
Innermost TRS:
Rules:
A__AND(tt, z0) -> c(MARK(z0))
A__AND(z0, z1) -> c1
A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
A__ISNATILIST(zeros) -> c3
A__ISNATILIST(cons(z0, z1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNAT(z0))
A__ISNATILIST(cons(z0, z1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNATILIST(z1))
A__ISNATILIST(z0) -> c6
A__ISNAT(0') -> c7
A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
A__ISNAT(z0) -> c10
A__ISNATLIST(nil) -> c11
A__ISNATLIST(cons(z0, z1)) -> c12(A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
A__ISNATLIST(cons(z0, z1)) -> c13(A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
A__ISNATLIST(take(z0, z1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNAT(z0))
A__ISNATLIST(take(z0, z1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNATILIST(z1))
A__ISNATLIST(z0) -> c16
A__ZEROS -> c17
A__ZEROS -> c18
A__TAKE(0', z0) -> c19(A__UTAKE1(a__isNatIList(z0)), A__ISNATILIST(z0))
A__TAKE(s(z0), cons(z1, z2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__ISNAT(z0))
A__TAKE(s(z0), cons(z1, z2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNAT(z1))
A__TAKE(s(z0), cons(z1, z2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNATILIST(z2))
A__TAKE(z0, z1) -> c23
A__UTAKE1(tt) -> c24
A__UTAKE1(z0) -> c25
A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
A__UTAKE2(z0, z1, z2, z3) -> c27
A__LENGTH(cons(z0, z1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
A__LENGTH(cons(z0, z1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
A__LENGTH(z0) -> c30
A__ULENGTH(tt, z0) -> c31(A__LENGTH(mark(z0)), MARK(z0))
A__ULENGTH(z0, z1) -> c32
MARK(and(z0, z1)) -> c33(A__AND(mark(z0), mark(z1)), MARK(z0))
MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1))
MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
MARK(isNat(z0)) -> c37(A__ISNAT(z0))
MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
MARK(zeros) -> c39(A__ZEROS)
MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
MARK(uTake1(z0)) -> c42(A__UTAKE1(mark(z0)), MARK(z0))
MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
MARK(tt) -> c45
MARK(0') -> c46
MARK(s(z0)) -> c47(MARK(z0))
MARK(cons(z0, z1)) -> c48(MARK(z0))
MARK(nil) -> c49
a__and(tt, z0) -> mark(z0)
a__and(z0, z1) -> and(z0, z1)
a__isNatIList(z0) -> a__isNatList(z0)
a__isNatIList(zeros) -> tt
a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
a__isNatIList(z0) -> isNatIList(z0)
a__isNat(0') -> tt
a__isNat(s(z0)) -> a__isNat(z0)
a__isNat(length(z0)) -> a__isNatList(z0)
a__isNat(z0) -> isNat(z0)
a__isNatList(nil) -> tt
a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
a__isNatList(z0) -> isNatList(z0)
a__zeros -> cons(0', zeros)
a__zeros -> zeros
a__take(0', z0) -> a__uTake1(a__isNatIList(z0))
a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
a__take(z0, z1) -> take(z0, z1)
a__uTake1(tt) -> nil
a__uTake1(z0) -> uTake1(z0)
a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
a__length(z0) -> length(z0)
a__uLength(tt, z0) -> s(a__length(mark(z0)))
a__uLength(z0, z1) -> uLength(z0, z1)
mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
mark(isNatIList(z0)) -> a__isNatIList(z0)
mark(isNatList(z0)) -> a__isNatList(z0)
mark(isNat(z0)) -> a__isNat(z0)
mark(length(z0)) -> a__length(mark(z0))
mark(zeros) -> a__zeros
mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
mark(uTake1(z0)) -> a__uTake1(mark(z0))
mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
mark(tt) -> tt
mark(0') -> 0'
mark(s(z0)) -> s(mark(z0))
mark(cons(z0, z1)) -> cons(mark(z0), z1)
mark(nil) -> nil

Types:
A__AND :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> c:c1
tt :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c :: c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49 -> c:c1
MARK :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
c1 :: c:c1
A__ISNATILIST :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> c2:c3:c4:c5:c6
c2 :: c11:c12:c13:c14:c15:c16 -> c2:c3:c4:c5:c6
A__ISNATLIST :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> c11:c12:c13:c14:c15:c16
zeros :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c3 :: c2:c3:c4:c5:c6
cons :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c4 :: c:c1 -> c7:c8:c9:c10 -> c2:c3:c4:c5:c6
a__isNat :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
a__isNatIList :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
A__ISNAT :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> c7:c8:c9:c10
c5 :: c:c1 -> c2:c3:c4:c5:c6 -> c2:c3:c4:c5:c6
c6 :: c2:c3:c4:c5:c6
0' :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c7 :: c7:c8:c9:c10
s :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c8 :: c7:c8:c9:c10 -> c7:c8:c9:c10
length :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c9 :: c11:c12:c13:c14:c15:c16 -> c7:c8:c9:c10
c10 :: c7:c8:c9:c10
nil :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c11 :: c11:c12:c13:c14:c15:c16
c12 :: c:c1 -> c7:c8:c9:c10 -> c11:c12:c13:c14:c15:c16
a__isNatList :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c13 :: c:c1 -> c11:c12:c13:c14:c15:c16 -> c11:c12:c13:c14:c15:c16
take :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c14 :: c:c1 -> c7:c8:c9:c10 -> c11:c12:c13:c14:c15:c16
c15 :: c:c1 -> c2:c3:c4:c5:c6 -> c11:c12:c13:c14:c15:c16
c16 :: c11:c12:c13:c14:c15:c16
A__ZEROS :: c17:c18
c17 :: c17:c18
c18 :: c17:c18
A__TAKE :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> c19:c20:c21:c22:c23
c19 :: c24:c25 -> c2:c3:c4:c5:c6 -> c19:c20:c21:c22:c23
A__UTAKE1 :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> c24:c25
c20 :: c26:c27 -> c:c1 -> c7:c8:c9:c10 -> c19:c20:c21:c22:c23
A__UTAKE2 :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> c26:c27
a__and :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c21 :: c26:c27 -> c:c1 -> c:c1 -> c7:c8:c9:c10 -> c19:c20:c21:c22:c23
c22 :: c26:c27 -> c:c1 -> c:c1 -> c2:c3:c4:c5:c6 -> c19:c20:c21:c22:c23
c23 :: c19:c20:c21:c22:c23
c24 :: c24:c25
c25 :: c24:c25
c26 :: c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49 -> c26:c27
c27 :: c26:c27
A__LENGTH :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> c28:c29:c30
c28 :: c31:c32 -> c:c1 -> c7:c8:c9:c10 -> c28:c29:c30
A__ULENGTH :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> c31:c32
c29 :: c31:c32 -> c:c1 -> c11:c12:c13:c14:c15:c16 -> c28:c29:c30
c30 :: c28:c29:c30
c31 :: c28:c29:c30 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49 -> c31:c32
mark :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c32 :: c31:c32
and :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c33 :: c:c1 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
c34 :: c:c1 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
isNatIList :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c35 :: c2:c3:c4:c5:c6 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
isNatList :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c36 :: c11:c12:c13:c14:c15:c16 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
isNat :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c37 :: c7:c8:c9:c10 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
c38 :: c28:c29:c30 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
c39 :: c17:c18 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
c40 :: c19:c20:c21:c22:c23 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
c41 :: c19:c20:c21:c22:c23 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
uTake1 :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c42 :: c24:c25 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
uTake2 :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c43 :: c26:c27 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
uLength :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c44 :: c31:c32 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
c45 :: c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
c46 :: c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
c47 :: c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
c48 :: c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
c49 :: c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
a__zeros :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
a__take :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
a__uTake1 :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
a__uTake2 :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
a__length :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
a__uLength :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
hole_c:c11_50 :: c:c1
hole_tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength2_50 :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
hole_c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c493_50 :: c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
hole_c2:c3:c4:c5:c64_50 :: c2:c3:c4:c5:c6
hole_c11:c12:c13:c14:c15:c165_50 :: c11:c12:c13:c14:c15:c16
hole_c7:c8:c9:c106_50 :: c7:c8:c9:c10
hole_c17:c187_50 :: c17:c18
hole_c19:c20:c21:c22:c238_50 :: c19:c20:c21:c22:c23
hole_c24:c259_50 :: c24:c25
hole_c26:c2710_50 :: c26:c27
hole_c28:c29:c3011_50 :: c28:c29:c30
hole_c31:c3212_50 :: c31:c32
gen_tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength13_50 :: Nat -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
gen_c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c4914_50 :: Nat -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
gen_c2:c3:c4:c5:c615_50 :: Nat -> c2:c3:c4:c5:c6
gen_c11:c12:c13:c14:c15:c1616_50 :: Nat -> c11:c12:c13:c14:c15:c16
gen_c7:c8:c9:c1017_50 :: Nat -> c7:c8:c9:c10


Lemmas:
a__isNatList(gen_tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength13_50(+(1, n19_50))) -> *18_50, rt in Omega(0)


Generator Equations:
gen_tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength13_50(0) <=> tt
gen_tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength13_50(+(x, 1)) <=> cons(tt, gen_tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength13_50(x))
gen_c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c4914_50(0) <=> c35(c2(c11))
gen_c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c4914_50(+(x, 1)) <=> c33(c(c35(c2(c11))), gen_c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c4914_50(x))
gen_c2:c3:c4:c5:c615_50(0) <=> c2(c11)
gen_c2:c3:c4:c5:c615_50(+(x, 1)) <=> c5(c(c35(c2(c11))), gen_c2:c3:c4:c5:c615_50(x))
gen_c11:c12:c13:c14:c15:c1616_50(0) <=> c11
gen_c11:c12:c13:c14:c15:c1616_50(+(x, 1)) <=> c13(c(c35(c2(c11))), gen_c11:c12:c13:c14:c15:c1616_50(x))
gen_c7:c8:c9:c1017_50(0) <=> c7
gen_c7:c8:c9:c1017_50(+(x, 1)) <=> c8(gen_c7:c8:c9:c1017_50(x))


The following defined symbols remain to be analysed:
a__and, A__AND, MARK, A__ISNATILIST, A__ISNATLIST, a__isNat, a__isNatIList, A__ISNAT, A__LENGTH, A__ULENGTH, mark, a__length, a__uLength

They will be analysed ascendingly in the following order:
A__AND = MARK
A__AND = A__ISNATILIST
A__AND = A__ISNATLIST
A__AND = A__ISNAT
A__AND = A__LENGTH
A__AND = A__ULENGTH
MARK = A__ISNATILIST
MARK = A__ISNATLIST
a__isNat < MARK
a__isNatIList < MARK
MARK = A__ISNAT
a__and < MARK
MARK = A__LENGTH
MARK = A__ULENGTH
mark < MARK
A__ISNATILIST = A__ISNATLIST
a__isNat < A__ISNATILIST
a__isNatIList < A__ISNATILIST
A__ISNATILIST = A__ISNAT
A__ISNATILIST = A__LENGTH
A__ISNATILIST = A__ULENGTH
a__isNat < A__ISNATLIST
a__isNatIList < A__ISNATLIST
A__ISNATLIST = A__ISNAT
a__isNatList < A__ISNATLIST
A__ISNATLIST = A__LENGTH
A__ISNATLIST = A__ULENGTH
a__isNat = a__isNatIList
a__isNat = a__isNatList
a__isNat = a__and
a__isNat < A__LENGTH
a__isNat = mark
a__isNat = a__length
a__isNat = a__uLength
a__isNatIList = a__isNatList
a__isNatIList = a__and
a__isNatIList = mark
a__isNatIList = a__length
a__isNatIList = a__uLength
A__ISNAT = A__LENGTH
A__ISNAT = A__ULENGTH
a__isNatList = a__and
a__isNatList < A__LENGTH
a__isNatList = mark
a__isNatList = a__length
a__isNatList = a__uLength
a__and < A__LENGTH
a__and = mark
a__and = a__length
a__and = a__uLength
A__LENGTH = A__ULENGTH
mark < A__ULENGTH
mark = a__length
mark = a__uLength
a__length = a__uLength

----------------------------------------

(17) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
a__isNatIList(gen_tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength13_50(+(1, n565563_50))) -> *18_50, rt in Omega(0)

Induction Base:
a__isNatIList(gen_tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength13_50(+(1, 0)))

Induction Step:
a__isNatIList(gen_tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength13_50(+(1, +(n565563_50, 1)))) ->_R^Omega(0)
a__and(a__isNat(tt), a__isNatIList(gen_tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength13_50(+(1, n565563_50)))) ->_R^Omega(0)
a__and(isNat(tt), a__isNatIList(gen_tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength13_50(+(1, n565563_50)))) ->_IH
a__and(isNat(tt), *18_50)

We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0).
----------------------------------------

(18)
Obligation:
Innermost TRS:
Rules:
A__AND(tt, z0) -> c(MARK(z0))
A__AND(z0, z1) -> c1
A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
A__ISNATILIST(zeros) -> c3
A__ISNATILIST(cons(z0, z1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNAT(z0))
A__ISNATILIST(cons(z0, z1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNATILIST(z1))
A__ISNATILIST(z0) -> c6
A__ISNAT(0') -> c7
A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
A__ISNAT(z0) -> c10
A__ISNATLIST(nil) -> c11
A__ISNATLIST(cons(z0, z1)) -> c12(A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
A__ISNATLIST(cons(z0, z1)) -> c13(A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
A__ISNATLIST(take(z0, z1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNAT(z0))
A__ISNATLIST(take(z0, z1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNATILIST(z1))
A__ISNATLIST(z0) -> c16
A__ZEROS -> c17
A__ZEROS -> c18
A__TAKE(0', z0) -> c19(A__UTAKE1(a__isNatIList(z0)), A__ISNATILIST(z0))
A__TAKE(s(z0), cons(z1, z2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__ISNAT(z0))
A__TAKE(s(z0), cons(z1, z2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNAT(z1))
A__TAKE(s(z0), cons(z1, z2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNATILIST(z2))
A__TAKE(z0, z1) -> c23
A__UTAKE1(tt) -> c24
A__UTAKE1(z0) -> c25
A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
A__UTAKE2(z0, z1, z2, z3) -> c27
A__LENGTH(cons(z0, z1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
A__LENGTH(cons(z0, z1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
A__LENGTH(z0) -> c30
A__ULENGTH(tt, z0) -> c31(A__LENGTH(mark(z0)), MARK(z0))
A__ULENGTH(z0, z1) -> c32
MARK(and(z0, z1)) -> c33(A__AND(mark(z0), mark(z1)), MARK(z0))
MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1))
MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
MARK(isNat(z0)) -> c37(A__ISNAT(z0))
MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
MARK(zeros) -> c39(A__ZEROS)
MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
MARK(uTake1(z0)) -> c42(A__UTAKE1(mark(z0)), MARK(z0))
MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
MARK(tt) -> c45
MARK(0') -> c46
MARK(s(z0)) -> c47(MARK(z0))
MARK(cons(z0, z1)) -> c48(MARK(z0))
MARK(nil) -> c49
a__and(tt, z0) -> mark(z0)
a__and(z0, z1) -> and(z0, z1)
a__isNatIList(z0) -> a__isNatList(z0)
a__isNatIList(zeros) -> tt
a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
a__isNatIList(z0) -> isNatIList(z0)
a__isNat(0') -> tt
a__isNat(s(z0)) -> a__isNat(z0)
a__isNat(length(z0)) -> a__isNatList(z0)
a__isNat(z0) -> isNat(z0)
a__isNatList(nil) -> tt
a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
a__isNatList(z0) -> isNatList(z0)
a__zeros -> cons(0', zeros)
a__zeros -> zeros
a__take(0', z0) -> a__uTake1(a__isNatIList(z0))
a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
a__take(z0, z1) -> take(z0, z1)
a__uTake1(tt) -> nil
a__uTake1(z0) -> uTake1(z0)
a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
a__length(z0) -> length(z0)
a__uLength(tt, z0) -> s(a__length(mark(z0)))
a__uLength(z0, z1) -> uLength(z0, z1)
mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
mark(isNatIList(z0)) -> a__isNatIList(z0)
mark(isNatList(z0)) -> a__isNatList(z0)
mark(isNat(z0)) -> a__isNat(z0)
mark(length(z0)) -> a__length(mark(z0))
mark(zeros) -> a__zeros
mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
mark(uTake1(z0)) -> a__uTake1(mark(z0))
mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
mark(tt) -> tt
mark(0') -> 0'
mark(s(z0)) -> s(mark(z0))
mark(cons(z0, z1)) -> cons(mark(z0), z1)
mark(nil) -> nil

Types:
A__AND :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> c:c1
tt :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c :: c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49 -> c:c1
MARK :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
c1 :: c:c1
A__ISNATILIST :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> c2:c3:c4:c5:c6
c2 :: c11:c12:c13:c14:c15:c16 -> c2:c3:c4:c5:c6
A__ISNATLIST :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> c11:c12:c13:c14:c15:c16
zeros :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c3 :: c2:c3:c4:c5:c6
cons :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c4 :: c:c1 -> c7:c8:c9:c10 -> c2:c3:c4:c5:c6
a__isNat :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
a__isNatIList :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
A__ISNAT :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> c7:c8:c9:c10
c5 :: c:c1 -> c2:c3:c4:c5:c6 -> c2:c3:c4:c5:c6
c6 :: c2:c3:c4:c5:c6
0' :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c7 :: c7:c8:c9:c10
s :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c8 :: c7:c8:c9:c10 -> c7:c8:c9:c10
length :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c9 :: c11:c12:c13:c14:c15:c16 -> c7:c8:c9:c10
c10 :: c7:c8:c9:c10
nil :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c11 :: c11:c12:c13:c14:c15:c16
c12 :: c:c1 -> c7:c8:c9:c10 -> c11:c12:c13:c14:c15:c16
a__isNatList :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c13 :: c:c1 -> c11:c12:c13:c14:c15:c16 -> c11:c12:c13:c14:c15:c16
take :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c14 :: c:c1 -> c7:c8:c9:c10 -> c11:c12:c13:c14:c15:c16
c15 :: c:c1 -> c2:c3:c4:c5:c6 -> c11:c12:c13:c14:c15:c16
c16 :: c11:c12:c13:c14:c15:c16
A__ZEROS :: c17:c18
c17 :: c17:c18
c18 :: c17:c18
A__TAKE :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> c19:c20:c21:c22:c23
c19 :: c24:c25 -> c2:c3:c4:c5:c6 -> c19:c20:c21:c22:c23
A__UTAKE1 :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> c24:c25
c20 :: c26:c27 -> c:c1 -> c7:c8:c9:c10 -> c19:c20:c21:c22:c23
A__UTAKE2 :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> c26:c27
a__and :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c21 :: c26:c27 -> c:c1 -> c:c1 -> c7:c8:c9:c10 -> c19:c20:c21:c22:c23
c22 :: c26:c27 -> c:c1 -> c:c1 -> c2:c3:c4:c5:c6 -> c19:c20:c21:c22:c23
c23 :: c19:c20:c21:c22:c23
c24 :: c24:c25
c25 :: c24:c25
c26 :: c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49 -> c26:c27
c27 :: c26:c27
A__LENGTH :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> c28:c29:c30
c28 :: c31:c32 -> c:c1 -> c7:c8:c9:c10 -> c28:c29:c30
A__ULENGTH :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> c31:c32
c29 :: c31:c32 -> c:c1 -> c11:c12:c13:c14:c15:c16 -> c28:c29:c30
c30 :: c28:c29:c30
c31 :: c28:c29:c30 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49 -> c31:c32
mark :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c32 :: c31:c32
and :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c33 :: c:c1 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
c34 :: c:c1 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
isNatIList :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c35 :: c2:c3:c4:c5:c6 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
isNatList :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c36 :: c11:c12:c13:c14:c15:c16 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
isNat :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c37 :: c7:c8:c9:c10 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
c38 :: c28:c29:c30 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
c39 :: c17:c18 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
c40 :: c19:c20:c21:c22:c23 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
c41 :: c19:c20:c21:c22:c23 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
uTake1 :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c42 :: c24:c25 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
uTake2 :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c43 :: c26:c27 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
uLength :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c44 :: c31:c32 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
c45 :: c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
c46 :: c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
c47 :: c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
c48 :: c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
c49 :: c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
a__zeros :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
a__take :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
a__uTake1 :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
a__uTake2 :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
a__length :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
a__uLength :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
hole_c:c11_50 :: c:c1
hole_tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength2_50 :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
hole_c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c493_50 :: c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
hole_c2:c3:c4:c5:c64_50 :: c2:c3:c4:c5:c6
hole_c11:c12:c13:c14:c15:c165_50 :: c11:c12:c13:c14:c15:c16
hole_c7:c8:c9:c106_50 :: c7:c8:c9:c10
hole_c17:c187_50 :: c17:c18
hole_c19:c20:c21:c22:c238_50 :: c19:c20:c21:c22:c23
hole_c24:c259_50 :: c24:c25
hole_c26:c2710_50 :: c26:c27
hole_c28:c29:c3011_50 :: c28:c29:c30
hole_c31:c3212_50 :: c31:c32
gen_tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength13_50 :: Nat -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
gen_c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c4914_50 :: Nat -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
gen_c2:c3:c4:c5:c615_50 :: Nat -> c2:c3:c4:c5:c6
gen_c11:c12:c13:c14:c15:c1616_50 :: Nat -> c11:c12:c13:c14:c15:c16
gen_c7:c8:c9:c1017_50 :: Nat -> c7:c8:c9:c10


Lemmas:
a__isNatList(gen_tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength13_50(+(1, n19_50))) -> *18_50, rt in Omega(0)
a__isNatIList(gen_tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength13_50(+(1, n565563_50))) -> *18_50, rt in Omega(0)


Generator Equations:
gen_tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength13_50(0) <=> tt
gen_tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength13_50(+(x, 1)) <=> cons(tt, gen_tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength13_50(x))
gen_c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c4914_50(0) <=> c35(c2(c11))
gen_c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c4914_50(+(x, 1)) <=> c33(c(c35(c2(c11))), gen_c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c4914_50(x))
gen_c2:c3:c4:c5:c615_50(0) <=> c2(c11)
gen_c2:c3:c4:c5:c615_50(+(x, 1)) <=> c5(c(c35(c2(c11))), gen_c2:c3:c4:c5:c615_50(x))
gen_c11:c12:c13:c14:c15:c1616_50(0) <=> c11
gen_c11:c12:c13:c14:c15:c1616_50(+(x, 1)) <=> c13(c(c35(c2(c11))), gen_c11:c12:c13:c14:c15:c1616_50(x))
gen_c7:c8:c9:c1017_50(0) <=> c7
gen_c7:c8:c9:c1017_50(+(x, 1)) <=> c8(gen_c7:c8:c9:c1017_50(x))


The following defined symbols remain to be analysed:
a__isNat, A__AND, MARK, A__ISNATILIST, A__ISNATLIST, A__ISNAT, a__isNatList, a__and, A__LENGTH, A__ULENGTH, mark, a__length, a__uLength

They will be analysed ascendingly in the following order:
A__AND = MARK
A__AND = A__ISNATILIST
A__AND = A__ISNATLIST
A__AND = A__ISNAT
A__AND = A__LENGTH
A__AND = A__ULENGTH
MARK = A__ISNATILIST
MARK = A__ISNATLIST
a__isNat < MARK
a__isNatIList < MARK
MARK = A__ISNAT
a__and < MARK
MARK = A__LENGTH
MARK = A__ULENGTH
mark < MARK
A__ISNATILIST = A__ISNATLIST
a__isNat < A__ISNATILIST
a__isNatIList < A__ISNATILIST
A__ISNATILIST = A__ISNAT
A__ISNATILIST = A__LENGTH
A__ISNATILIST = A__ULENGTH
a__isNat < A__ISNATLIST
a__isNatIList < A__ISNATLIST
A__ISNATLIST = A__ISNAT
a__isNatList < A__ISNATLIST
A__ISNATLIST = A__LENGTH
A__ISNATLIST = A__ULENGTH
a__isNat = a__isNatIList
a__isNat = a__isNatList
a__isNat = a__and
a__isNat < A__LENGTH
a__isNat = mark
a__isNat = a__length
a__isNat = a__uLength
a__isNatIList = a__isNatList
a__isNatIList = a__and
a__isNatIList = mark
a__isNatIList = a__length
a__isNatIList = a__uLength
A__ISNAT = A__LENGTH
A__ISNAT = A__ULENGTH
a__isNatList = a__and
a__isNatList < A__LENGTH
a__isNatList = mark
a__isNatList = a__length
a__isNatList = a__uLength
a__and < A__LENGTH
a__and = mark
a__and = a__length
a__and = a__uLength
A__LENGTH = A__ULENGTH
mark < A__ULENGTH
mark = a__length
mark = a__uLength
a__length = a__uLength

----------------------------------------

(19) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
a__isNatList(gen_tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength13_50(+(1, n859962_50))) -> *18_50, rt in Omega(0)

Induction Base:
a__isNatList(gen_tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength13_50(+(1, 0)))

Induction Step:
a__isNatList(gen_tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength13_50(+(1, +(n859962_50, 1)))) ->_R^Omega(0)
a__and(a__isNat(tt), a__isNatList(gen_tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength13_50(+(1, n859962_50)))) ->_R^Omega(0)
a__and(isNat(tt), a__isNatList(gen_tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength13_50(+(1, n859962_50)))) ->_IH
a__and(isNat(tt), *18_50)

We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0).
----------------------------------------

(20)
Obligation:
Innermost TRS:
Rules:
A__AND(tt, z0) -> c(MARK(z0))
A__AND(z0, z1) -> c1
A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
A__ISNATILIST(zeros) -> c3
A__ISNATILIST(cons(z0, z1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNAT(z0))
A__ISNATILIST(cons(z0, z1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNATILIST(z1))
A__ISNATILIST(z0) -> c6
A__ISNAT(0') -> c7
A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
A__ISNAT(z0) -> c10
A__ISNATLIST(nil) -> c11
A__ISNATLIST(cons(z0, z1)) -> c12(A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
A__ISNATLIST(cons(z0, z1)) -> c13(A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
A__ISNATLIST(take(z0, z1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNAT(z0))
A__ISNATLIST(take(z0, z1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNATILIST(z1))
A__ISNATLIST(z0) -> c16
A__ZEROS -> c17
A__ZEROS -> c18
A__TAKE(0', z0) -> c19(A__UTAKE1(a__isNatIList(z0)), A__ISNATILIST(z0))
A__TAKE(s(z0), cons(z1, z2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__ISNAT(z0))
A__TAKE(s(z0), cons(z1, z2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNAT(z1))
A__TAKE(s(z0), cons(z1, z2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNATILIST(z2))
A__TAKE(z0, z1) -> c23
A__UTAKE1(tt) -> c24
A__UTAKE1(z0) -> c25
A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
A__UTAKE2(z0, z1, z2, z3) -> c27
A__LENGTH(cons(z0, z1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
A__LENGTH(cons(z0, z1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
A__LENGTH(z0) -> c30
A__ULENGTH(tt, z0) -> c31(A__LENGTH(mark(z0)), MARK(z0))
A__ULENGTH(z0, z1) -> c32
MARK(and(z0, z1)) -> c33(A__AND(mark(z0), mark(z1)), MARK(z0))
MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1))
MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
MARK(isNat(z0)) -> c37(A__ISNAT(z0))
MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
MARK(zeros) -> c39(A__ZEROS)
MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
MARK(uTake1(z0)) -> c42(A__UTAKE1(mark(z0)), MARK(z0))
MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
MARK(tt) -> c45
MARK(0') -> c46
MARK(s(z0)) -> c47(MARK(z0))
MARK(cons(z0, z1)) -> c48(MARK(z0))
MARK(nil) -> c49
a__and(tt, z0) -> mark(z0)
a__and(z0, z1) -> and(z0, z1)
a__isNatIList(z0) -> a__isNatList(z0)
a__isNatIList(zeros) -> tt
a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
a__isNatIList(z0) -> isNatIList(z0)
a__isNat(0') -> tt
a__isNat(s(z0)) -> a__isNat(z0)
a__isNat(length(z0)) -> a__isNatList(z0)
a__isNat(z0) -> isNat(z0)
a__isNatList(nil) -> tt
a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
a__isNatList(z0) -> isNatList(z0)
a__zeros -> cons(0', zeros)
a__zeros -> zeros
a__take(0', z0) -> a__uTake1(a__isNatIList(z0))
a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
a__take(z0, z1) -> take(z0, z1)
a__uTake1(tt) -> nil
a__uTake1(z0) -> uTake1(z0)
a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
a__length(z0) -> length(z0)
a__uLength(tt, z0) -> s(a__length(mark(z0)))
a__uLength(z0, z1) -> uLength(z0, z1)
mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
mark(isNatIList(z0)) -> a__isNatIList(z0)
mark(isNatList(z0)) -> a__isNatList(z0)
mark(isNat(z0)) -> a__isNat(z0)
mark(length(z0)) -> a__length(mark(z0))
mark(zeros) -> a__zeros
mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
mark(uTake1(z0)) -> a__uTake1(mark(z0))
mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
mark(tt) -> tt
mark(0') -> 0'
mark(s(z0)) -> s(mark(z0))
mark(cons(z0, z1)) -> cons(mark(z0), z1)
mark(nil) -> nil

Types:
A__AND :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> c:c1
tt :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c :: c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49 -> c:c1
MARK :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
c1 :: c:c1
A__ISNATILIST :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> c2:c3:c4:c5:c6
c2 :: c11:c12:c13:c14:c15:c16 -> c2:c3:c4:c5:c6
A__ISNATLIST :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> c11:c12:c13:c14:c15:c16
zeros :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c3 :: c2:c3:c4:c5:c6
cons :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c4 :: c:c1 -> c7:c8:c9:c10 -> c2:c3:c4:c5:c6
a__isNat :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
a__isNatIList :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
A__ISNAT :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> c7:c8:c9:c10
c5 :: c:c1 -> c2:c3:c4:c5:c6 -> c2:c3:c4:c5:c6
c6 :: c2:c3:c4:c5:c6
0' :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c7 :: c7:c8:c9:c10
s :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c8 :: c7:c8:c9:c10 -> c7:c8:c9:c10
length :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c9 :: c11:c12:c13:c14:c15:c16 -> c7:c8:c9:c10
c10 :: c7:c8:c9:c10
nil :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c11 :: c11:c12:c13:c14:c15:c16
c12 :: c:c1 -> c7:c8:c9:c10 -> c11:c12:c13:c14:c15:c16
a__isNatList :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c13 :: c:c1 -> c11:c12:c13:c14:c15:c16 -> c11:c12:c13:c14:c15:c16
take :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c14 :: c:c1 -> c7:c8:c9:c10 -> c11:c12:c13:c14:c15:c16
c15 :: c:c1 -> c2:c3:c4:c5:c6 -> c11:c12:c13:c14:c15:c16
c16 :: c11:c12:c13:c14:c15:c16
A__ZEROS :: c17:c18
c17 :: c17:c18
c18 :: c17:c18
A__TAKE :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> c19:c20:c21:c22:c23
c19 :: c24:c25 -> c2:c3:c4:c5:c6 -> c19:c20:c21:c22:c23
A__UTAKE1 :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> c24:c25
c20 :: c26:c27 -> c:c1 -> c7:c8:c9:c10 -> c19:c20:c21:c22:c23
A__UTAKE2 :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> c26:c27
a__and :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c21 :: c26:c27 -> c:c1 -> c:c1 -> c7:c8:c9:c10 -> c19:c20:c21:c22:c23
c22 :: c26:c27 -> c:c1 -> c:c1 -> c2:c3:c4:c5:c6 -> c19:c20:c21:c22:c23
c23 :: c19:c20:c21:c22:c23
c24 :: c24:c25
c25 :: c24:c25
c26 :: c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49 -> c26:c27
c27 :: c26:c27
A__LENGTH :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> c28:c29:c30
c28 :: c31:c32 -> c:c1 -> c7:c8:c9:c10 -> c28:c29:c30
A__ULENGTH :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> c31:c32
c29 :: c31:c32 -> c:c1 -> c11:c12:c13:c14:c15:c16 -> c28:c29:c30
c30 :: c28:c29:c30
c31 :: c28:c29:c30 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49 -> c31:c32
mark :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c32 :: c31:c32
and :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c33 :: c:c1 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
c34 :: c:c1 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
isNatIList :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c35 :: c2:c3:c4:c5:c6 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
isNatList :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c36 :: c11:c12:c13:c14:c15:c16 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
isNat :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c37 :: c7:c8:c9:c10 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
c38 :: c28:c29:c30 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
c39 :: c17:c18 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
c40 :: c19:c20:c21:c22:c23 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
c41 :: c19:c20:c21:c22:c23 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
uTake1 :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c42 :: c24:c25 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
uTake2 :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c43 :: c26:c27 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
uLength :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
c44 :: c31:c32 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
c45 :: c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
c46 :: c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
c47 :: c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
c48 :: c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49 -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
c49 :: c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
a__zeros :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
a__take :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
a__uTake1 :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
a__uTake2 :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
a__length :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
a__uLength :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
hole_c:c11_50 :: c:c1
hole_tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength2_50 :: tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
hole_c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c493_50 :: c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
hole_c2:c3:c4:c5:c64_50 :: c2:c3:c4:c5:c6
hole_c11:c12:c13:c14:c15:c165_50 :: c11:c12:c13:c14:c15:c16
hole_c7:c8:c9:c106_50 :: c7:c8:c9:c10
hole_c17:c187_50 :: c17:c18
hole_c19:c20:c21:c22:c238_50 :: c19:c20:c21:c22:c23
hole_c24:c259_50 :: c24:c25
hole_c26:c2710_50 :: c26:c27
hole_c28:c29:c3011_50 :: c28:c29:c30
hole_c31:c3212_50 :: c31:c32
gen_tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength13_50 :: Nat -> tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
gen_c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c4914_50 :: Nat -> c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49
gen_c2:c3:c4:c5:c615_50 :: Nat -> c2:c3:c4:c5:c6
gen_c11:c12:c13:c14:c15:c1616_50 :: Nat -> c11:c12:c13:c14:c15:c16
gen_c7:c8:c9:c1017_50 :: Nat -> c7:c8:c9:c10


Lemmas:
a__isNatList(gen_tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength13_50(+(1, n859962_50))) -> *18_50, rt in Omega(0)
a__isNatIList(gen_tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength13_50(+(1, n565563_50))) -> *18_50, rt in Omega(0)


Generator Equations:
gen_tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength13_50(0) <=> tt
gen_tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength13_50(+(x, 1)) <=> cons(tt, gen_tt:zeros:cons:0':s:length:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength13_50(x))
gen_c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c4914_50(0) <=> c35(c2(c11))
gen_c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c4914_50(+(x, 1)) <=> c33(c(c35(c2(c11))), gen_c33:c34:c35:c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c4914_50(x))
gen_c2:c3:c4:c5:c615_50(0) <=> c2(c11)
gen_c2:c3:c4:c5:c615_50(+(x, 1)) <=> c5(c(c35(c2(c11))), gen_c2:c3:c4:c5:c615_50(x))
gen_c11:c12:c13:c14:c15:c1616_50(0) <=> c11
gen_c11:c12:c13:c14:c15:c1616_50(+(x, 1)) <=> c13(c(c35(c2(c11))), gen_c11:c12:c13:c14:c15:c1616_50(x))
gen_c7:c8:c9:c1017_50(0) <=> c7
gen_c7:c8:c9:c1017_50(+(x, 1)) <=> c8(gen_c7:c8:c9:c1017_50(x))


The following defined symbols remain to be analysed:
a__and, A__AND, MARK, A__ISNATILIST, A__ISNATLIST, A__ISNAT, A__LENGTH, A__ULENGTH, mark

They will be analysed ascendingly in the following order:
A__AND = MARK
A__AND = A__ISNATILIST
A__AND = A__ISNATLIST
A__AND = A__ISNAT
A__AND = A__LENGTH
A__AND = A__ULENGTH
MARK = A__ISNATILIST
MARK = A__ISNATLIST
a__isNat < MARK
a__isNatIList < MARK
MARK = A__ISNAT
a__and < MARK
MARK = A__LENGTH
MARK = A__ULENGTH
mark < MARK
A__ISNATILIST = A__ISNATLIST
a__isNat < A__ISNATILIST
a__isNatIList < A__ISNATILIST
A__ISNATILIST = A__ISNAT
A__ISNATILIST = A__LENGTH
A__ISNATILIST = A__ULENGTH
a__isNat < A__ISNATLIST
a__isNatIList < A__ISNATLIST
A__ISNATLIST = A__ISNAT
a__isNatList < A__ISNATLIST
A__ISNATLIST = A__LENGTH
A__ISNATLIST = A__ULENGTH
a__isNat = a__isNatIList
a__isNat = a__isNatList
a__isNat = a__and
a__isNat < A__LENGTH
a__isNat = mark
a__isNat = a__length
a__isNat = a__uLength
a__isNatIList = a__isNatList
a__isNatIList = a__and
a__isNatIList = mark
a__isNatIList = a__length
a__isNatIList = a__uLength
A__ISNAT = A__LENGTH
A__ISNAT = A__ULENGTH
a__isNatList = a__and
a__isNatList < A__LENGTH
a__isNatList = mark
a__isNatList = a__length
a__isNatList = a__uLength
a__and < A__LENGTH
a__and = mark
a__and = a__length
a__and = a__uLength
A__LENGTH = A__ULENGTH
mark < A__ULENGTH
mark = a__length
mark = a__uLength
a__length = a__uLength

----------------------------------------

(21) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
Transformed a relative TRS into a decreasing-loop problem.
----------------------------------------

(22)
Obligation:
Analyzing the following TRS for decreasing loops:

The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF).


The TRS R consists of the following rules:

   A__AND(tt, z0) -> c(MARK(z0))
   A__AND(z0, z1) -> c1
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNATILIST(zeros) -> c3
   A__ISNATILIST(cons(z0, z1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNAT(z0))
   A__ISNATILIST(cons(z0, z1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNATILIST(z1))
   A__ISNATILIST(z0) -> c6
   A__ISNAT(0) -> c7
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__ISNAT(z0) -> c10
   A__ISNATLIST(nil) -> c11
   A__ISNATLIST(cons(z0, z1)) -> c12(A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
   A__ISNATLIST(cons(z0, z1)) -> c13(A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__ISNATLIST(take(z0, z1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNAT(z0))
   A__ISNATLIST(take(z0, z1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNATILIST(z1))
   A__ISNATLIST(z0) -> c16
   A__ZEROS -> c17
   A__ZEROS -> c18
   A__TAKE(0, z0) -> c19(A__UTAKE1(a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(z0), cons(z1, z2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__ISNAT(z0))
   A__TAKE(s(z0), cons(z1, z2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNAT(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNATILIST(z2))
   A__TAKE(z0, z1) -> c23
   A__UTAKE1(tt) -> c24
   A__UTAKE1(z0) -> c25
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   A__UTAKE2(z0, z1, z2, z3) -> c27
   A__LENGTH(cons(z0, z1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
   A__LENGTH(cons(z0, z1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__LENGTH(z0) -> c30
   A__ULENGTH(tt, z0) -> c31(A__LENGTH(mark(z0)), MARK(z0))
   A__ULENGTH(z0, z1) -> c32
   MARK(and(z0, z1)) -> c33(A__AND(mark(z0), mark(z1)), MARK(z0))
   MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
   MARK(zeros) -> c39(A__ZEROS)
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake1(z0)) -> c42(A__UTAKE1(mark(z0)), MARK(z0))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(tt) -> c45
   MARK(0) -> c46
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   MARK(nil) -> c49

The (relative) TRS S consists of the following rules:

   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil

Rewrite Strategy: INNERMOST
----------------------------------------

(23) RelTrsToWeightedTrsProof (UPPER BOUND(ID))
Transformed relative TRS to weighted TRS
----------------------------------------

(24)
Obligation:
The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, INF).


The TRS R consists of the following rules:

   a__and(tt, T) -> mark(T) [1]
   a__isNatIList(IL) -> a__isNatList(IL) [1]
   a__isNat(0) -> tt [1]
   a__isNat(s(N)) -> a__isNat(N) [1]
   a__isNat(length(L)) -> a__isNatList(L) [1]
   a__isNatIList(zeros) -> tt [1]
   a__isNatIList(cons(N, IL)) -> a__and(a__isNat(N), a__isNatIList(IL)) [1]
   a__isNatList(nil) -> tt [1]
   a__isNatList(cons(N, L)) -> a__and(a__isNat(N), a__isNatList(L)) [1]
   a__isNatList(take(N, IL)) -> a__and(a__isNat(N), a__isNatIList(IL)) [1]
   a__zeros -> cons(0, zeros) [1]
   a__take(0, IL) -> a__uTake1(a__isNatIList(IL)) [1]
   a__uTake1(tt) -> nil [1]
   a__take(s(M), cons(N, IL)) -> a__uTake2(a__and(a__isNat(M), a__and(a__isNat(N), a__isNatIList(IL))), M, N, IL) [1]
   a__uTake2(tt, M, N, IL) -> cons(mark(N), take(M, IL)) [1]
   a__length(cons(N, L)) -> a__uLength(a__and(a__isNat(N), a__isNatList(L)), L) [1]
   a__uLength(tt, L) -> s(a__length(mark(L))) [1]
   mark(and(X1, X2)) -> a__and(mark(X1), mark(X2)) [1]
   mark(isNatIList(X)) -> a__isNatIList(X) [1]
   mark(isNatList(X)) -> a__isNatList(X) [1]
   mark(isNat(X)) -> a__isNat(X) [1]
   mark(length(X)) -> a__length(mark(X)) [1]
   mark(zeros) -> a__zeros [1]
   mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)) [1]
   mark(uTake1(X)) -> a__uTake1(mark(X)) [1]
   mark(uTake2(X1, X2, X3, X4)) -> a__uTake2(mark(X1), X2, X3, X4) [1]
   mark(uLength(X1, X2)) -> a__uLength(mark(X1), X2) [1]
   mark(tt) -> tt [1]
   mark(0) -> 0 [1]
   mark(s(X)) -> s(mark(X)) [1]
   mark(cons(X1, X2)) -> cons(mark(X1), X2) [1]
   mark(nil) -> nil [1]
   a__and(X1, X2) -> and(X1, X2) [1]
   a__isNatIList(X) -> isNatIList(X) [1]
   a__isNatList(X) -> isNatList(X) [1]
   a__isNat(X) -> isNat(X) [1]
   a__length(X) -> length(X) [1]
   a__zeros -> zeros [1]
   a__take(X1, X2) -> take(X1, X2) [1]
   a__uTake1(X) -> uTake1(X) [1]
   a__uTake2(X1, X2, X3, X4) -> uTake2(X1, X2, X3, X4) [1]
   a__uLength(X1, X2) -> uLength(X1, X2) [1]

Rewrite Strategy: INNERMOST
----------------------------------------

(25) TypeInferenceProof (BOTH BOUNDS(ID, ID))
Infered types.
----------------------------------------

(26)
Obligation:
Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   a__and(tt, T) -> mark(T) [1]
   a__isNatIList(IL) -> a__isNatList(IL) [1]
   a__isNat(0) -> tt [1]
   a__isNat(s(N)) -> a__isNat(N) [1]
   a__isNat(length(L)) -> a__isNatList(L) [1]
   a__isNatIList(zeros) -> tt [1]
   a__isNatIList(cons(N, IL)) -> a__and(a__isNat(N), a__isNatIList(IL)) [1]
   a__isNatList(nil) -> tt [1]
   a__isNatList(cons(N, L)) -> a__and(a__isNat(N), a__isNatList(L)) [1]
   a__isNatList(take(N, IL)) -> a__and(a__isNat(N), a__isNatIList(IL)) [1]
   a__zeros -> cons(0, zeros) [1]
   a__take(0, IL) -> a__uTake1(a__isNatIList(IL)) [1]
   a__uTake1(tt) -> nil [1]
   a__take(s(M), cons(N, IL)) -> a__uTake2(a__and(a__isNat(M), a__and(a__isNat(N), a__isNatIList(IL))), M, N, IL) [1]
   a__uTake2(tt, M, N, IL) -> cons(mark(N), take(M, IL)) [1]
   a__length(cons(N, L)) -> a__uLength(a__and(a__isNat(N), a__isNatList(L)), L) [1]
   a__uLength(tt, L) -> s(a__length(mark(L))) [1]
   mark(and(X1, X2)) -> a__and(mark(X1), mark(X2)) [1]
   mark(isNatIList(X)) -> a__isNatIList(X) [1]
   mark(isNatList(X)) -> a__isNatList(X) [1]
   mark(isNat(X)) -> a__isNat(X) [1]
   mark(length(X)) -> a__length(mark(X)) [1]
   mark(zeros) -> a__zeros [1]
   mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)) [1]
   mark(uTake1(X)) -> a__uTake1(mark(X)) [1]
   mark(uTake2(X1, X2, X3, X4)) -> a__uTake2(mark(X1), X2, X3, X4) [1]
   mark(uLength(X1, X2)) -> a__uLength(mark(X1), X2) [1]
   mark(tt) -> tt [1]
   mark(0) -> 0 [1]
   mark(s(X)) -> s(mark(X)) [1]
   mark(cons(X1, X2)) -> cons(mark(X1), X2) [1]
   mark(nil) -> nil [1]
   a__and(X1, X2) -> and(X1, X2) [1]
   a__isNatIList(X) -> isNatIList(X) [1]
   a__isNatList(X) -> isNatList(X) [1]
   a__isNat(X) -> isNat(X) [1]
   a__length(X) -> length(X) [1]
   a__zeros -> zeros [1]
   a__take(X1, X2) -> take(X1, X2) [1]
   a__uTake1(X) -> uTake1(X) [1]
   a__uTake2(X1, X2, X3, X4) -> uTake2(X1, X2, X3, X4) [1]
   a__uLength(X1, X2) -> uLength(X1, X2) [1]

The TRS has the following type information:
a__and :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
tt :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
mark :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
a__isNatIList :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
a__isNatList :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
a__isNat :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
0 :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
s :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
length :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
zeros :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
cons :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
nil :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
take :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
a__zeros :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
a__take :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
a__uTake1 :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
a__uTake2 :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
a__length :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
a__uLength :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
and :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
isNatIList :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
isNatList :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
isNat :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
uTake1 :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
uTake2 :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
uLength :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength

Rewrite Strategy: INNERMOST
----------------------------------------

(27) 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

----------------------------------------

(28)
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__and(tt, T) -> mark(T) [1]
   a__isNatIList(IL) -> a__isNatList(IL) [1]
   a__isNat(0) -> tt [1]
   a__isNat(s(N)) -> a__isNat(N) [1]
   a__isNat(length(L)) -> a__isNatList(L) [1]
   a__isNatIList(zeros) -> tt [1]
   a__isNatIList(cons(N, IL)) -> a__and(a__isNat(N), a__isNatIList(IL)) [1]
   a__isNatList(nil) -> tt [1]
   a__isNatList(cons(N, L)) -> a__and(a__isNat(N), a__isNatList(L)) [1]
   a__isNatList(take(N, IL)) -> a__and(a__isNat(N), a__isNatIList(IL)) [1]
   a__zeros -> cons(0, zeros) [1]
   a__take(0, IL) -> a__uTake1(a__isNatIList(IL)) [1]
   a__uTake1(tt) -> nil [1]
   a__take(s(M), cons(N, IL)) -> a__uTake2(a__and(a__isNat(M), a__and(a__isNat(N), a__isNatIList(IL))), M, N, IL) [1]
   a__uTake2(tt, M, N, IL) -> cons(mark(N), take(M, IL)) [1]
   a__length(cons(N, L)) -> a__uLength(a__and(a__isNat(N), a__isNatList(L)), L) [1]
   a__uLength(tt, L) -> s(a__length(mark(L))) [1]
   mark(and(X1, X2)) -> a__and(mark(X1), mark(X2)) [1]
   mark(isNatIList(X)) -> a__isNatIList(X) [1]
   mark(isNatList(X)) -> a__isNatList(X) [1]
   mark(isNat(X)) -> a__isNat(X) [1]
   mark(length(X)) -> a__length(mark(X)) [1]
   mark(zeros) -> a__zeros [1]
   mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)) [1]
   mark(uTake1(X)) -> a__uTake1(mark(X)) [1]
   mark(uTake2(X1, X2, X3, X4)) -> a__uTake2(mark(X1), X2, X3, X4) [1]
   mark(uLength(X1, X2)) -> a__uLength(mark(X1), X2) [1]
   mark(tt) -> tt [1]
   mark(0) -> 0 [1]
   mark(s(X)) -> s(mark(X)) [1]
   mark(cons(X1, X2)) -> cons(mark(X1), X2) [1]
   mark(nil) -> nil [1]
   a__and(X1, X2) -> and(X1, X2) [1]
   a__isNatIList(X) -> isNatIList(X) [1]
   a__isNatList(X) -> isNatList(X) [1]
   a__isNat(X) -> isNat(X) [1]
   a__length(X) -> length(X) [1]
   a__zeros -> zeros [1]
   a__take(X1, X2) -> take(X1, X2) [1]
   a__uTake1(X) -> uTake1(X) [1]
   a__uTake2(X1, X2, X3, X4) -> uTake2(X1, X2, X3, X4) [1]
   a__uLength(X1, X2) -> uLength(X1, X2) [1]

The TRS has the following type information:
a__and :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
tt :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
mark :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
a__isNatIList :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
a__isNatList :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
a__isNat :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
0 :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
s :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
length :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
zeros :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
cons :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
nil :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
take :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
a__zeros :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
a__take :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
a__uTake1 :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
a__uTake2 :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
a__length :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
a__uLength :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
and :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
isNatIList :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
isNatList :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
isNat :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
uTake1 :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
uTake2 :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
uLength :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength

Rewrite Strategy: INNERMOST
----------------------------------------

(29) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID))
Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction.
The constant constructors are abstracted as follows:

   tt => 2
   0 => 0
   zeros => 3
   nil => 1

----------------------------------------

(30)
Obligation:
Complexity RNTS consisting of the following rules:

   a__and(z, z') -{ 1 }-> mark(T) :|: z = 2, z' = T, T >= 0
   a__and(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   a__isNat(z) -{ 1 }-> a__isNatList(L) :|: z = 1 + L, L >= 0
   a__isNat(z) -{ 1 }-> a__isNat(N) :|: z = 1 + N, N >= 0
   a__isNat(z) -{ 1 }-> 2 :|: z = 0
   a__isNat(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__isNatIList(z) -{ 1 }-> a__isNatList(IL) :|: z = IL, IL >= 0
   a__isNatIList(z) -{ 1 }-> a__and(a__isNat(N), a__isNatIList(IL)) :|: z = 1 + N + IL, IL >= 0, N >= 0
   a__isNatIList(z) -{ 1 }-> 2 :|: z = 3
   a__isNatIList(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__isNatList(z) -{ 1 }-> a__and(a__isNat(N), a__isNatList(L)) :|: z = 1 + N + L, L >= 0, N >= 0
   a__isNatList(z) -{ 1 }-> a__and(a__isNat(N), a__isNatIList(IL)) :|: z = 1 + N + IL, IL >= 0, N >= 0
   a__isNatList(z) -{ 1 }-> 2 :|: z = 1
   a__isNatList(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__length(z) -{ 1 }-> a__uLength(a__and(a__isNat(N), a__isNatList(L)), L) :|: z = 1 + N + L, L >= 0, N >= 0
   a__length(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__take(z, z') -{ 1 }-> a__uTake2(a__and(a__isNat(M), a__and(a__isNat(N), a__isNatIList(IL))), M, N, IL) :|: z = 1 + M, M >= 0, IL >= 0, z' = 1 + N + IL, N >= 0
   a__take(z, z') -{ 1 }-> a__uTake1(a__isNatIList(IL)) :|: z' = IL, z = 0, IL >= 0
   a__take(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   a__uLength(z, z') -{ 1 }-> 1 + a__length(mark(L)) :|: z = 2, L >= 0, z' = L
   a__uLength(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   a__uTake1(z) -{ 1 }-> 1 :|: z = 2
   a__uTake1(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__uTake2(z, z', z'', z1) -{ 1 }-> 1 + mark(N) + (1 + M + IL) :|: z = 2, z' = M, z1 = IL, z'' = N, M >= 0, IL >= 0, N >= 0
   a__uTake2(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__zeros -{ 1 }-> 3 :|: 
   a__zeros -{ 1 }-> 1 + 0 + 3 :|: 
   mark(z) -{ 1 }-> a__zeros :|: z = 3
   mark(z) -{ 1 }-> a__uTake2(mark(X1), X2, X3, X4) :|: X1 >= 0, z = 1 + X1 + X2 + X3 + X4, X3 >= 0, X2 >= 0, X4 >= 0
   mark(z) -{ 1 }-> a__uTake1(mark(X)) :|: z = 1 + X, X >= 0
   mark(z) -{ 1 }-> a__uLength(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   mark(z) -{ 1 }-> a__take(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   mark(z) -{ 1 }-> a__length(mark(X)) :|: z = 1 + X, X >= 0
   mark(z) -{ 1 }-> a__isNatList(X) :|: z = 1 + X, X >= 0
   mark(z) -{ 1 }-> a__isNatIList(X) :|: z = 1 + X, X >= 0
   mark(z) -{ 1 }-> a__isNat(X) :|: z = 1 + X, X >= 0
   mark(z) -{ 1 }-> a__and(mark(X1), mark(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.

----------------------------------------

(31) 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__isNat_1
   a__isNatIList_1
   a__and_2
   a__isNatList_1
   a__uLength_2
   a__uTake1_1
   a__length_1
   a__uTake2_4
   a__take_2
   a__zeros

Due to the following rules being added:
none

And the following fresh constants: none

----------------------------------------

(32)
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__and(tt, T) -> mark(T) [1]
   a__isNatIList(IL) -> a__isNatList(IL) [1]
   a__isNat(0) -> tt [1]
   a__isNat(s(N)) -> a__isNat(N) [1]
   a__isNat(length(L)) -> a__isNatList(L) [1]
   a__isNatIList(zeros) -> tt [1]
   a__isNatIList(cons(N, IL)) -> a__and(a__isNat(N), a__isNatIList(IL)) [1]
   a__isNatList(nil) -> tt [1]
   a__isNatList(cons(N, L)) -> a__and(a__isNat(N), a__isNatList(L)) [1]
   a__isNatList(take(N, IL)) -> a__and(a__isNat(N), a__isNatIList(IL)) [1]
   a__zeros -> cons(0, zeros) [1]
   a__take(0, IL) -> a__uTake1(a__isNatIList(IL)) [1]
   a__uTake1(tt) -> nil [1]
   a__take(s(M), cons(N, IL)) -> a__uTake2(a__and(a__isNat(M), a__and(a__isNat(N), a__isNatIList(IL))), M, N, IL) [1]
   a__uTake2(tt, M, N, IL) -> cons(mark(N), take(M, IL)) [1]
   a__length(cons(N, L)) -> a__uLength(a__and(a__isNat(N), a__isNatList(L)), L) [1]
   a__uLength(tt, L) -> s(a__length(mark(L))) [1]
   mark(and(X1, X2)) -> a__and(mark(X1), mark(X2)) [1]
   mark(isNatIList(X)) -> a__isNatIList(X) [1]
   mark(isNatList(X)) -> a__isNatList(X) [1]
   mark(isNat(X)) -> a__isNat(X) [1]
   mark(length(X)) -> a__length(mark(X)) [1]
   mark(zeros) -> a__zeros [1]
   mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)) [1]
   mark(uTake1(X)) -> a__uTake1(mark(X)) [1]
   mark(uTake2(X1, X2, X3, X4)) -> a__uTake2(mark(X1), X2, X3, X4) [1]
   mark(uLength(X1, X2)) -> a__uLength(mark(X1), X2) [1]
   mark(tt) -> tt [1]
   mark(0) -> 0 [1]
   mark(s(X)) -> s(mark(X)) [1]
   mark(cons(X1, X2)) -> cons(mark(X1), X2) [1]
   mark(nil) -> nil [1]
   a__and(X1, X2) -> and(X1, X2) [1]
   a__isNatIList(X) -> isNatIList(X) [1]
   a__isNatList(X) -> isNatList(X) [1]
   a__isNat(X) -> isNat(X) [1]
   a__length(X) -> length(X) [1]
   a__zeros -> zeros [1]
   a__take(X1, X2) -> take(X1, X2) [1]
   a__uTake1(X) -> uTake1(X) [1]
   a__uTake2(X1, X2, X3, X4) -> uTake2(X1, X2, X3, X4) [1]
   a__uLength(X1, X2) -> uLength(X1, X2) [1]

The TRS has the following type information:
a__and :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
tt :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
mark :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
a__isNatIList :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
a__isNatList :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
a__isNat :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
0 :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
s :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
length :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
zeros :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
cons :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
nil :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
take :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
a__zeros :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
a__take :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
a__uTake1 :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
a__uTake2 :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
a__length :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
a__uLength :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
and :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
isNatIList :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
isNatList :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
isNat :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
uTake1 :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
uTake2 :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
uLength :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength

Rewrite Strategy: INNERMOST
----------------------------------------

(33) NarrowingProof (BOTH BOUNDS(ID, ID))
Narrowed the inner basic terms of all right-hand sides by a single narrowing step.
----------------------------------------

(34)
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__and(tt, T) -> mark(T) [1]
   a__isNatIList(IL) -> a__isNatList(IL) [1]
   a__isNat(0) -> tt [1]
   a__isNat(s(N)) -> a__isNat(N) [1]
   a__isNat(length(L)) -> a__isNatList(L) [1]
   a__isNatIList(zeros) -> tt [1]
   a__isNatIList(cons(0, IL)) -> a__and(tt, a__isNatList(IL)) [3]
   a__isNatIList(cons(0, zeros)) -> a__and(tt, tt) [3]
   a__isNatIList(cons(0, cons(N'', IL'))) -> a__and(tt, a__and(a__isNat(N''), a__isNatIList(IL'))) [3]
   a__isNatIList(cons(0, IL)) -> a__and(tt, isNatIList(IL)) [3]
   a__isNatIList(cons(s(N'), IL)) -> a__and(a__isNat(N'), a__isNatList(IL)) [3]
   a__isNatIList(cons(s(N'), zeros)) -> a__and(a__isNat(N'), tt) [3]
   a__isNatIList(cons(s(N'), cons(N1, IL''))) -> a__and(a__isNat(N'), a__and(a__isNat(N1), a__isNatIList(IL''))) [3]
   a__isNatIList(cons(s(N'), IL)) -> a__and(a__isNat(N'), isNatIList(IL)) [3]
   a__isNatIList(cons(length(L'), IL)) -> a__and(a__isNatList(L'), a__isNatList(IL)) [3]
   a__isNatIList(cons(length(L'), zeros)) -> a__and(a__isNatList(L'), tt) [3]
   a__isNatIList(cons(length(L'), cons(N2, IL1))) -> a__and(a__isNatList(L'), a__and(a__isNat(N2), a__isNatIList(IL1))) [3]
   a__isNatIList(cons(length(L'), IL)) -> a__and(a__isNatList(L'), isNatIList(IL)) [3]
   a__isNatIList(cons(N, IL)) -> a__and(isNat(N), a__isNatList(IL)) [3]
   a__isNatIList(cons(N, zeros)) -> a__and(isNat(N), tt) [3]
   a__isNatIList(cons(N, cons(N3, IL2))) -> a__and(isNat(N), a__and(a__isNat(N3), a__isNatIList(IL2))) [3]
   a__isNatIList(cons(N, IL)) -> a__and(isNat(N), isNatIList(IL)) [3]
   a__isNatList(nil) -> tt [1]
   a__isNatList(cons(0, nil)) -> a__and(tt, tt) [3]
   a__isNatList(cons(0, cons(N5, L1))) -> a__and(tt, a__and(a__isNat(N5), a__isNatList(L1))) [3]
   a__isNatList(cons(0, take(N6, IL3))) -> a__and(tt, a__and(a__isNat(N6), a__isNatIList(IL3))) [3]
   a__isNatList(cons(0, L)) -> a__and(tt, isNatList(L)) [3]
   a__isNatList(cons(s(N4), nil)) -> a__and(a__isNat(N4), tt) [3]
   a__isNatList(cons(s(N4), cons(N7, L2))) -> a__and(a__isNat(N4), a__and(a__isNat(N7), a__isNatList(L2))) [3]
   a__isNatList(cons(s(N4), take(N8, IL4))) -> a__and(a__isNat(N4), a__and(a__isNat(N8), a__isNatIList(IL4))) [3]
   a__isNatList(cons(s(N4), L)) -> a__and(a__isNat(N4), isNatList(L)) [3]
   a__isNatList(cons(length(L''), nil)) -> a__and(a__isNatList(L''), tt) [3]
   a__isNatList(cons(length(L''), cons(N9, L3))) -> a__and(a__isNatList(L''), a__and(a__isNat(N9), a__isNatList(L3))) [3]
   a__isNatList(cons(length(L''), take(N10, IL5))) -> a__and(a__isNatList(L''), a__and(a__isNat(N10), a__isNatIList(IL5))) [3]
   a__isNatList(cons(length(L''), L)) -> a__and(a__isNatList(L''), isNatList(L)) [3]
   a__isNatList(cons(N, nil)) -> a__and(isNat(N), tt) [3]
   a__isNatList(cons(N, cons(N11, L4))) -> a__and(isNat(N), a__and(a__isNat(N11), a__isNatList(L4))) [3]
   a__isNatList(cons(N, take(N12, IL6))) -> a__and(isNat(N), a__and(a__isNat(N12), a__isNatIList(IL6))) [3]
   a__isNatList(cons(N, L)) -> a__and(isNat(N), isNatList(L)) [3]
   a__isNatList(take(0, IL)) -> a__and(tt, a__isNatList(IL)) [3]
   a__isNatList(take(0, zeros)) -> a__and(tt, tt) [3]
   a__isNatList(take(0, cons(N14, IL7))) -> a__and(tt, a__and(a__isNat(N14), a__isNatIList(IL7))) [3]
   a__isNatList(take(0, IL)) -> a__and(tt, isNatIList(IL)) [3]
   a__isNatList(take(s(N13), IL)) -> a__and(a__isNat(N13), a__isNatList(IL)) [3]
   a__isNatList(take(s(N13), zeros)) -> a__and(a__isNat(N13), tt) [3]
   a__isNatList(take(s(N13), cons(N15, IL8))) -> a__and(a__isNat(N13), a__and(a__isNat(N15), a__isNatIList(IL8))) [3]
   a__isNatList(take(s(N13), IL)) -> a__and(a__isNat(N13), isNatIList(IL)) [3]
   a__isNatList(take(length(L5), IL)) -> a__and(a__isNatList(L5), a__isNatList(IL)) [3]
   a__isNatList(take(length(L5), zeros)) -> a__and(a__isNatList(L5), tt) [3]
   a__isNatList(take(length(L5), cons(N16, IL9))) -> a__and(a__isNatList(L5), a__and(a__isNat(N16), a__isNatIList(IL9))) [3]
   a__isNatList(take(length(L5), IL)) -> a__and(a__isNatList(L5), isNatIList(IL)) [3]
   a__isNatList(take(N, IL)) -> a__and(isNat(N), a__isNatList(IL)) [3]
   a__isNatList(take(N, zeros)) -> a__and(isNat(N), tt) [3]
   a__isNatList(take(N, cons(N17, IL10))) -> a__and(isNat(N), a__and(a__isNat(N17), a__isNatIList(IL10))) [3]
   a__isNatList(take(N, IL)) -> a__and(isNat(N), isNatIList(IL)) [3]
   a__zeros -> cons(0, zeros) [1]
   a__take(0, IL) -> a__uTake1(a__isNatList(IL)) [2]
   a__take(0, zeros) -> a__uTake1(tt) [2]
   a__take(0, cons(N18, IL11)) -> a__uTake1(a__and(a__isNat(N18), a__isNatIList(IL11))) [2]
   a__take(0, IL) -> a__uTake1(isNatIList(IL)) [2]
   a__uTake1(tt) -> nil [1]
   a__take(s(M), cons(N, IL)) -> a__uTake2(a__and(a__isNat(M), a__and(a__isNat(N), a__isNatIList(IL))), M, N, IL) [1]
   a__uTake2(tt, M, N, IL) -> cons(mark(N), take(M, IL)) [1]
   a__length(cons(0, nil)) -> a__uLength(a__and(tt, tt), nil) [3]
   a__length(cons(0, cons(N41, L12))) -> a__uLength(a__and(tt, a__and(a__isNat(N41), a__isNatList(L12))), cons(N41, L12)) [3]
   a__length(cons(0, take(N42, IL28))) -> a__uLength(a__and(tt, a__and(a__isNat(N42), a__isNatIList(IL28))), take(N42, IL28)) [3]
   a__length(cons(0, L)) -> a__uLength(a__and(tt, isNatList(L)), L) [3]
   a__length(cons(s(N40), nil)) -> a__uLength(a__and(a__isNat(N40), tt), nil) [3]
   a__length(cons(s(N40), cons(N43, L13))) -> a__uLength(a__and(a__isNat(N40), a__and(a__isNat(N43), a__isNatList(L13))), cons(N43, L13)) [3]
   a__length(cons(s(N40), take(N44, IL29))) -> a__uLength(a__and(a__isNat(N40), a__and(a__isNat(N44), a__isNatIList(IL29))), take(N44, IL29)) [3]
   a__length(cons(s(N40), L)) -> a__uLength(a__and(a__isNat(N40), isNatList(L)), L) [3]
   a__length(cons(length(L11), nil)) -> a__uLength(a__and(a__isNatList(L11), tt), nil) [3]
   a__length(cons(length(L11), cons(N45, L14))) -> a__uLength(a__and(a__isNatList(L11), a__and(a__isNat(N45), a__isNatList(L14))), cons(N45, L14)) [3]
   a__length(cons(length(L11), take(N46, IL30))) -> a__uLength(a__and(a__isNatList(L11), a__and(a__isNat(N46), a__isNatIList(IL30))), take(N46, IL30)) [3]
   a__length(cons(length(L11), L)) -> a__uLength(a__and(a__isNatList(L11), isNatList(L)), L) [3]
   a__length(cons(N, nil)) -> a__uLength(a__and(isNat(N), tt), nil) [3]
   a__length(cons(N, cons(N47, L15))) -> a__uLength(a__and(isNat(N), a__and(a__isNat(N47), a__isNatList(L15))), cons(N47, L15)) [3]
   a__length(cons(N, take(N48, IL31))) -> a__uLength(a__and(isNat(N), a__and(a__isNat(N48), a__isNatIList(IL31))), take(N48, IL31)) [3]
   a__length(cons(N, L)) -> a__uLength(a__and(isNat(N), isNatList(L)), L) [3]
   a__uLength(tt, and(X1', X2')) -> s(a__length(a__and(mark(X1'), mark(X2')))) [2]
   a__uLength(tt, isNatIList(X')) -> s(a__length(a__isNatIList(X'))) [2]
   a__uLength(tt, isNatList(X'')) -> s(a__length(a__isNatList(X''))) [2]
   a__uLength(tt, isNat(X5)) -> s(a__length(a__isNat(X5))) [2]
   a__uLength(tt, length(X6)) -> s(a__length(a__length(mark(X6)))) [2]
   a__uLength(tt, zeros) -> s(a__length(a__zeros)) [2]
   a__uLength(tt, take(X1'', X2'')) -> s(a__length(a__take(mark(X1''), mark(X2'')))) [2]
   a__uLength(tt, uTake1(X7)) -> s(a__length(a__uTake1(mark(X7)))) [2]
   a__uLength(tt, uTake2(X11, X21, X3', X4')) -> s(a__length(a__uTake2(mark(X11), X21, X3', X4'))) [2]
   a__uLength(tt, uLength(X12, X22)) -> s(a__length(a__uLength(mark(X12), X22))) [2]
   a__uLength(tt, tt) -> s(a__length(tt)) [2]
   a__uLength(tt, 0) -> s(a__length(0)) [2]
   a__uLength(tt, s(X8)) -> s(a__length(s(mark(X8)))) [2]
   a__uLength(tt, cons(X13, X23)) -> s(a__length(cons(mark(X13), X23))) [2]
   a__uLength(tt, nil) -> s(a__length(nil)) [2]
   mark(and(X1, X2)) -> a__and(mark(X1), mark(X2)) [1]
   mark(isNatIList(X)) -> a__isNatIList(X) [1]
   mark(isNatList(X)) -> a__isNatList(X) [1]
   mark(isNat(X)) -> a__isNat(X) [1]
   mark(length(and(X1100, X284))) -> a__length(a__and(mark(X1100), mark(X284))) [2]
   mark(length(isNatIList(X200))) -> a__length(a__isNatIList(X200)) [2]
   mark(length(isNatList(X201))) -> a__length(a__isNatList(X201)) [2]
   mark(length(isNat(X202))) -> a__length(a__isNat(X202)) [2]
   mark(length(length(X203))) -> a__length(a__length(mark(X203))) [2]
   mark(length(zeros)) -> a__length(a__zeros) [2]
   mark(length(take(X1101, X285))) -> a__length(a__take(mark(X1101), mark(X285))) [2]
   mark(length(uTake1(X204))) -> a__length(a__uTake1(mark(X204))) [2]
   mark(length(uTake2(X1102, X286, X324, X423))) -> a__length(a__uTake2(mark(X1102), X286, X324, X423)) [2]
   mark(length(uLength(X1103, X287))) -> a__length(a__uLength(mark(X1103), X287)) [2]
   mark(length(tt)) -> a__length(tt) [2]
   mark(length(0)) -> a__length(0) [2]
   mark(length(s(X205))) -> a__length(s(mark(X205))) [2]
   mark(length(cons(X1104, X288))) -> a__length(cons(mark(X1104), X288)) [2]
   mark(length(nil)) -> a__length(nil) [2]
   mark(zeros) -> a__zeros [1]
   mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)) [1]
   mark(uTake1(and(X1185, X2174))) -> a__uTake1(a__and(mark(X1185), mark(X2174))) [2]
   mark(uTake1(isNatIList(X445))) -> a__uTake1(a__isNatIList(X445)) [2]
   mark(uTake1(isNatList(X446))) -> a__uTake1(a__isNatList(X446)) [2]
   mark(uTake1(isNat(X447))) -> a__uTake1(a__isNat(X447)) [2]
   mark(uTake1(length(X448))) -> a__uTake1(a__length(mark(X448))) [2]
   mark(uTake1(zeros)) -> a__uTake1(a__zeros) [2]
   mark(uTake1(take(X1186, X2175))) -> a__uTake1(a__take(mark(X1186), mark(X2175))) [2]
   mark(uTake1(uTake1(X449))) -> a__uTake1(a__uTake1(mark(X449))) [2]
   mark(uTake1(uTake2(X1187, X2176, X3103, X450))) -> a__uTake1(a__uTake2(mark(X1187), X2176, X3103, X450)) [2]
   mark(uTake1(uLength(X1188, X2177))) -> a__uTake1(a__uLength(mark(X1188), X2177)) [2]
   mark(uTake1(tt)) -> a__uTake1(tt) [2]
   mark(uTake1(0)) -> a__uTake1(0) [2]
   mark(uTake1(s(X451))) -> a__uTake1(s(mark(X451))) [2]
   mark(uTake1(cons(X1189, X2178))) -> a__uTake1(cons(mark(X1189), X2178)) [2]
   mark(uTake1(nil)) -> a__uTake1(nil) [2]
   mark(uTake2(and(X1190, X2179), X2, X3, X4)) -> a__uTake2(a__and(mark(X1190), mark(X2179)), X2, X3, X4) [2]
   mark(uTake2(isNatIList(X452), X2, X3, X4)) -> a__uTake2(a__isNatIList(X452), X2, X3, X4) [2]
   mark(uTake2(isNatList(X453), X2, X3, X4)) -> a__uTake2(a__isNatList(X453), X2, X3, X4) [2]
   mark(uTake2(isNat(X454), X2, X3, X4)) -> a__uTake2(a__isNat(X454), X2, X3, X4) [2]
   mark(uTake2(length(X455), X2, X3, X4)) -> a__uTake2(a__length(mark(X455)), X2, X3, X4) [2]
   mark(uTake2(zeros, X2, X3, X4)) -> a__uTake2(a__zeros, X2, X3, X4) [2]
   mark(uTake2(take(X1191, X2180), X2, X3, X4)) -> a__uTake2(a__take(mark(X1191), mark(X2180)), X2, X3, X4) [2]
   mark(uTake2(uTake1(X456), X2, X3, X4)) -> a__uTake2(a__uTake1(mark(X456)), X2, X3, X4) [2]
   mark(uTake2(uTake2(X1192, X2181, X3104, X457), X2, X3, X4)) -> a__uTake2(a__uTake2(mark(X1192), X2181, X3104, X457), X2, X3, X4) [2]
   mark(uTake2(uLength(X1193, X2182), X2, X3, X4)) -> a__uTake2(a__uLength(mark(X1193), X2182), X2, X3, X4) [2]
   mark(uTake2(tt, X2, X3, X4)) -> a__uTake2(tt, X2, X3, X4) [2]
   mark(uTake2(0, X2, X3, X4)) -> a__uTake2(0, X2, X3, X4) [2]
   mark(uTake2(s(X458), X2, X3, X4)) -> a__uTake2(s(mark(X458)), X2, X3, X4) [2]
   mark(uTake2(cons(X1194, X2183), X2, X3, X4)) -> a__uTake2(cons(mark(X1194), X2183), X2, X3, X4) [2]
   mark(uTake2(nil, X2, X3, X4)) -> a__uTake2(nil, X2, X3, X4) [2]
   mark(uLength(and(X1195, X2184), X2)) -> a__uLength(a__and(mark(X1195), mark(X2184)), X2) [2]
   mark(uLength(isNatIList(X459), X2)) -> a__uLength(a__isNatIList(X459), X2) [2]
   mark(uLength(isNatList(X460), X2)) -> a__uLength(a__isNatList(X460), X2) [2]
   mark(uLength(isNat(X461), X2)) -> a__uLength(a__isNat(X461), X2) [2]
   mark(uLength(length(X462), X2)) -> a__uLength(a__length(mark(X462)), X2) [2]
   mark(uLength(zeros, X2)) -> a__uLength(a__zeros, X2) [2]
   mark(uLength(take(X1196, X2185), X2)) -> a__uLength(a__take(mark(X1196), mark(X2185)), X2) [2]
   mark(uLength(uTake1(X463), X2)) -> a__uLength(a__uTake1(mark(X463)), X2) [2]
   mark(uLength(uTake2(X1197, X2186, X3105, X464), X2)) -> a__uLength(a__uTake2(mark(X1197), X2186, X3105, X464), X2) [2]
   mark(uLength(uLength(X1198, X2187), X2)) -> a__uLength(a__uLength(mark(X1198), X2187), X2) [2]
   mark(uLength(tt, X2)) -> a__uLength(tt, X2) [2]
   mark(uLength(0, X2)) -> a__uLength(0, X2) [2]
   mark(uLength(s(X465), X2)) -> a__uLength(s(mark(X465)), X2) [2]
   mark(uLength(cons(X1199, X2188), X2)) -> a__uLength(cons(mark(X1199), X2188), X2) [2]
   mark(uLength(nil, X2)) -> a__uLength(nil, X2) [2]
   mark(tt) -> tt [1]
   mark(0) -> 0 [1]
   mark(s(X)) -> s(mark(X)) [1]
   mark(cons(X1, X2)) -> cons(mark(X1), X2) [1]
   mark(nil) -> nil [1]
   a__and(X1, X2) -> and(X1, X2) [1]
   a__isNatIList(X) -> isNatIList(X) [1]
   a__isNatList(X) -> isNatList(X) [1]
   a__isNat(X) -> isNat(X) [1]
   a__length(X) -> length(X) [1]
   a__zeros -> zeros [1]
   a__take(X1, X2) -> take(X1, X2) [1]
   a__uTake1(X) -> uTake1(X) [1]
   a__uTake2(X1, X2, X3, X4) -> uTake2(X1, X2, X3, X4) [1]
   a__uLength(X1, X2) -> uLength(X1, X2) [1]

The TRS has the following type information:
a__and :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
tt :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
mark :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
a__isNatIList :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
a__isNatList :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
a__isNat :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
0 :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
s :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
length :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
zeros :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
cons :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
nil :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
take :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
a__zeros :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
a__take :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
a__uTake1 :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
a__uTake2 :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
a__length :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
a__uLength :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
and :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
isNatIList :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
isNatList :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
isNat :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
uTake1 :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
uTake2 :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength
uLength :: tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength -> tt:0:s:length:zeros:cons:nil:take:and:isNatIList:isNatList:isNat:uTake1:uTake2:uLength

Rewrite Strategy: INNERMOST
----------------------------------------

(35) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID))
Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction.
The constant constructors are abstracted as follows:

   tt => 2
   0 => 0
   zeros => 3
   nil => 1

----------------------------------------

(36)
Obligation:
Complexity RNTS consisting of the following rules:

   a__and(z, z') -{ 1 }-> mark(T) :|: z = 2, z' = T, T >= 0
   a__and(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   a__isNat(z) -{ 1 }-> a__isNatList(L) :|: z = 1 + L, L >= 0
   a__isNat(z) -{ 1 }-> a__isNat(N) :|: z = 1 + N, N >= 0
   a__isNat(z) -{ 1 }-> 2 :|: z = 0
   a__isNat(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__isNatIList(z) -{ 1 }-> a__isNatList(IL) :|: z = IL, IL >= 0
   a__isNatIList(z) -{ 3 }-> a__and(a__isNatList(L'), a__isNatList(IL)) :|: L' >= 0, z = 1 + (1 + L') + IL, IL >= 0
   a__isNatIList(z) -{ 3 }-> a__and(a__isNatList(L'), a__and(a__isNat(N2), a__isNatIList(IL1))) :|: L' >= 0, IL1 >= 0, z = 1 + (1 + L') + (1 + N2 + IL1), N2 >= 0
   a__isNatIList(z) -{ 3 }-> a__and(a__isNatList(L'), 2) :|: L' >= 0, z = 1 + (1 + L') + 3
   a__isNatIList(z) -{ 3 }-> a__and(a__isNatList(L'), 1 + IL) :|: L' >= 0, z = 1 + (1 + L') + IL, IL >= 0
   a__isNatIList(z) -{ 3 }-> a__and(a__isNat(N'), a__isNatList(IL)) :|: N' >= 0, z = 1 + (1 + N') + IL, IL >= 0
   a__isNatIList(z) -{ 3 }-> a__and(a__isNat(N'), a__and(a__isNat(N1), a__isNatIList(IL''))) :|: IL'' >= 0, N1 >= 0, z = 1 + (1 + N') + (1 + N1 + IL''), N' >= 0
   a__isNatIList(z) -{ 3 }-> a__and(a__isNat(N'), 2) :|: z = 1 + (1 + N') + 3, N' >= 0
   a__isNatIList(z) -{ 3 }-> a__and(a__isNat(N'), 1 + IL) :|: N' >= 0, z = 1 + (1 + N') + IL, IL >= 0
   a__isNatIList(z) -{ 3 }-> a__and(2, a__isNatList(IL)) :|: z = 1 + 0 + IL, IL >= 0
   a__isNatIList(z) -{ 3 }-> a__and(2, a__and(a__isNat(N''), a__isNatIList(IL'))) :|: IL' >= 0, z = 1 + 0 + (1 + N'' + IL'), N'' >= 0
   a__isNatIList(z) -{ 3 }-> a__and(2, 2) :|: z = 1 + 0 + 3
   a__isNatIList(z) -{ 3 }-> a__and(2, 1 + IL) :|: z = 1 + 0 + IL, IL >= 0
   a__isNatIList(z) -{ 3 }-> a__and(1 + N, a__isNatList(IL)) :|: z = 1 + N + IL, IL >= 0, N >= 0
   a__isNatIList(z) -{ 3 }-> a__and(1 + N, a__and(a__isNat(N3), a__isNatIList(IL2))) :|: IL2 >= 0, N3 >= 0, z = 1 + N + (1 + N3 + IL2), N >= 0
   a__isNatIList(z) -{ 3 }-> a__and(1 + N, 2) :|: z = 1 + N + 3, N >= 0
   a__isNatIList(z) -{ 3 }-> a__and(1 + N, 1 + IL) :|: z = 1 + N + IL, IL >= 0, N >= 0
   a__isNatIList(z) -{ 1 }-> 2 :|: z = 3
   a__isNatIList(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__isNatList(z) -{ 3 }-> a__and(a__isNatList(L''), a__and(a__isNat(N10), a__isNatIList(IL5))) :|: L'' >= 0, z = 1 + (1 + L'') + (1 + N10 + IL5), N10 >= 0, IL5 >= 0
   a__isNatList(z) -{ 3 }-> a__and(a__isNatList(L''), a__and(a__isNat(N9), a__isNatList(L3))) :|: L3 >= 0, z = 1 + (1 + L'') + (1 + N9 + L3), N9 >= 0, L'' >= 0
   a__isNatList(z) -{ 3 }-> a__and(a__isNatList(L''), 2) :|: z = 1 + (1 + L'') + 1, L'' >= 0
   a__isNatList(z) -{ 3 }-> a__and(a__isNatList(L''), 1 + L) :|: z = 1 + (1 + L'') + L, L'' >= 0, L >= 0
   a__isNatList(z) -{ 3 }-> a__and(a__isNatList(L5), a__isNatList(IL)) :|: z = 1 + (1 + L5) + IL, L5 >= 0, IL >= 0
   a__isNatList(z) -{ 3 }-> a__and(a__isNatList(L5), a__and(a__isNat(N16), a__isNatIList(IL9))) :|: IL9 >= 0, L5 >= 0, N16 >= 0, z = 1 + (1 + L5) + (1 + N16 + IL9)
   a__isNatList(z) -{ 3 }-> a__and(a__isNatList(L5), 2) :|: L5 >= 0, z = 1 + (1 + L5) + 3
   a__isNatList(z) -{ 3 }-> a__and(a__isNatList(L5), 1 + IL) :|: z = 1 + (1 + L5) + IL, L5 >= 0, IL >= 0
   a__isNatList(z) -{ 3 }-> a__and(a__isNat(N13), a__isNatList(IL)) :|: z = 1 + (1 + N13) + IL, N13 >= 0, IL >= 0
   a__isNatList(z) -{ 3 }-> a__and(a__isNat(N13), a__and(a__isNat(N15), a__isNatIList(IL8))) :|: N15 >= 0, z = 1 + (1 + N13) + (1 + N15 + IL8), IL8 >= 0, N13 >= 0
   a__isNatList(z) -{ 3 }-> a__and(a__isNat(N13), 2) :|: z = 1 + (1 + N13) + 3, N13 >= 0
   a__isNatList(z) -{ 3 }-> a__and(a__isNat(N13), 1 + IL) :|: z = 1 + (1 + N13) + IL, N13 >= 0, IL >= 0
   a__isNatList(z) -{ 3 }-> a__and(a__isNat(N4), a__and(a__isNat(N7), a__isNatList(L2))) :|: z = 1 + (1 + N4) + (1 + N7 + L2), N7 >= 0, L2 >= 0, N4 >= 0
   a__isNatList(z) -{ 3 }-> a__and(a__isNat(N4), a__and(a__isNat(N8), a__isNatIList(IL4))) :|: z = 1 + (1 + N4) + (1 + N8 + IL4), N8 >= 0, IL4 >= 0, N4 >= 0
   a__isNatList(z) -{ 3 }-> a__and(a__isNat(N4), 2) :|: z = 1 + (1 + N4) + 1, N4 >= 0
   a__isNatList(z) -{ 3 }-> a__and(a__isNat(N4), 1 + L) :|: z = 1 + (1 + N4) + L, L >= 0, N4 >= 0
   a__isNatList(z) -{ 3 }-> a__and(2, a__isNatList(IL)) :|: z = 1 + 0 + IL, IL >= 0
   a__isNatList(z) -{ 3 }-> a__and(2, a__and(a__isNat(N14), a__isNatIList(IL7))) :|: IL7 >= 0, N14 >= 0, z = 1 + 0 + (1 + N14 + IL7)
   a__isNatList(z) -{ 3 }-> a__and(2, a__and(a__isNat(N5), a__isNatList(L1))) :|: z = 1 + 0 + (1 + N5 + L1), L1 >= 0, N5 >= 0
   a__isNatList(z) -{ 3 }-> a__and(2, a__and(a__isNat(N6), a__isNatIList(IL3))) :|: IL3 >= 0, z = 1 + 0 + (1 + N6 + IL3), N6 >= 0
   a__isNatList(z) -{ 3 }-> a__and(2, 2) :|: z = 1 + 0 + 1
   a__isNatList(z) -{ 3 }-> a__and(2, 2) :|: z = 1 + 0 + 3
   a__isNatList(z) -{ 3 }-> a__and(2, 1 + IL) :|: z = 1 + 0 + IL, IL >= 0
   a__isNatList(z) -{ 3 }-> a__and(2, 1 + L) :|: z = 1 + 0 + L, L >= 0
   a__isNatList(z) -{ 3 }-> a__and(1 + N, a__isNatList(IL)) :|: z = 1 + N + IL, IL >= 0, N >= 0
   a__isNatList(z) -{ 3 }-> a__and(1 + N, a__and(a__isNat(N11), a__isNatList(L4))) :|: N11 >= 0, z = 1 + N + (1 + N11 + L4), N >= 0, L4 >= 0
   a__isNatList(z) -{ 3 }-> a__and(1 + N, a__and(a__isNat(N12), a__isNatIList(IL6))) :|: z = 1 + N + (1 + N12 + IL6), N12 >= 0, IL6 >= 0, N >= 0
   a__isNatList(z) -{ 3 }-> a__and(1 + N, a__and(a__isNat(N17), a__isNatIList(IL10))) :|: z = 1 + N + (1 + N17 + IL10), IL10 >= 0, N17 >= 0, N >= 0
   a__isNatList(z) -{ 3 }-> a__and(1 + N, 2) :|: z = 1 + N + 1, N >= 0
   a__isNatList(z) -{ 3 }-> a__and(1 + N, 2) :|: z = 1 + N + 3, N >= 0
   a__isNatList(z) -{ 3 }-> a__and(1 + N, 1 + IL) :|: z = 1 + N + IL, IL >= 0, N >= 0
   a__isNatList(z) -{ 3 }-> a__and(1 + N, 1 + L) :|: z = 1 + N + L, L >= 0, N >= 0
   a__isNatList(z) -{ 1 }-> 2 :|: z = 1
   a__isNatList(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__length(z) -{ 3 }-> a__uLength(a__and(a__isNatList(L11), a__and(a__isNat(N45), a__isNatList(L14))), 1 + N45 + L14) :|: z = 1 + (1 + L11) + (1 + N45 + L14), N45 >= 0, L11 >= 0, L14 >= 0
   a__length(z) -{ 3 }-> a__uLength(a__and(a__isNatList(L11), a__and(a__isNat(N46), a__isNatIList(IL30))), 1 + N46 + IL30) :|: N46 >= 0, IL30 >= 0, L11 >= 0, z = 1 + (1 + L11) + (1 + N46 + IL30)
   a__length(z) -{ 3 }-> a__uLength(a__and(a__isNatList(L11), 2), 1) :|: z = 1 + (1 + L11) + 1, L11 >= 0
   a__length(z) -{ 3 }-> a__uLength(a__and(a__isNatList(L11), 1 + L), L) :|: z = 1 + (1 + L11) + L, L11 >= 0, L >= 0
   a__length(z) -{ 3 }-> a__uLength(a__and(a__isNat(N40), a__and(a__isNat(N43), a__isNatList(L13))), 1 + N43 + L13) :|: L13 >= 0, N43 >= 0, z = 1 + (1 + N40) + (1 + N43 + L13), N40 >= 0
   a__length(z) -{ 3 }-> a__uLength(a__and(a__isNat(N40), a__and(a__isNat(N44), a__isNatIList(IL29))), 1 + N44 + IL29) :|: IL29 >= 0, z = 1 + (1 + N40) + (1 + N44 + IL29), N44 >= 0, N40 >= 0
   a__length(z) -{ 3 }-> a__uLength(a__and(a__isNat(N40), 2), 1) :|: z = 1 + (1 + N40) + 1, N40 >= 0
   a__length(z) -{ 3 }-> a__uLength(a__and(a__isNat(N40), 1 + L), L) :|: z = 1 + (1 + N40) + L, L >= 0, N40 >= 0
   a__length(z) -{ 3 }-> a__uLength(a__and(2, a__and(a__isNat(N41), a__isNatList(L12))), 1 + N41 + L12) :|: z = 1 + 0 + (1 + N41 + L12), L12 >= 0, N41 >= 0
   a__length(z) -{ 3 }-> a__uLength(a__and(2, a__and(a__isNat(N42), a__isNatIList(IL28))), 1 + N42 + IL28) :|: N42 >= 0, IL28 >= 0, z = 1 + 0 + (1 + N42 + IL28)
   a__length(z) -{ 3 }-> a__uLength(a__and(2, 2), 1) :|: z = 1 + 0 + 1
   a__length(z) -{ 3 }-> a__uLength(a__and(2, 1 + L), L) :|: z = 1 + 0 + L, L >= 0
   a__length(z) -{ 3 }-> a__uLength(a__and(1 + N, a__and(a__isNat(N47), a__isNatList(L15))), 1 + N47 + L15) :|: z = 1 + N + (1 + N47 + L15), L15 >= 0, N47 >= 0, N >= 0
   a__length(z) -{ 3 }-> a__uLength(a__and(1 + N, a__and(a__isNat(N48), a__isNatIList(IL31))), 1 + N48 + IL31) :|: IL31 >= 0, N48 >= 0, z = 1 + N + (1 + N48 + IL31), N >= 0
   a__length(z) -{ 3 }-> a__uLength(a__and(1 + N, 2), 1) :|: z = 1 + N + 1, N >= 0
   a__length(z) -{ 3 }-> a__uLength(a__and(1 + N, 1 + L), L) :|: z = 1 + N + L, L >= 0, N >= 0
   a__length(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__take(z, z') -{ 1 }-> a__uTake2(a__and(a__isNat(M), a__and(a__isNat(N), a__isNatIList(IL))), M, N, IL) :|: z = 1 + M, M >= 0, IL >= 0, z' = 1 + N + IL, N >= 0
   a__take(z, z') -{ 2 }-> a__uTake1(a__isNatList(IL)) :|: z' = IL, z = 0, IL >= 0
   a__take(z, z') -{ 2 }-> a__uTake1(a__and(a__isNat(N18), a__isNatIList(IL11))) :|: IL11 >= 0, z' = 1 + N18 + IL11, z = 0, N18 >= 0
   a__take(z, z') -{ 2 }-> a__uTake1(2) :|: z' = 3, z = 0
   a__take(z, z') -{ 2 }-> a__uTake1(1 + IL) :|: z' = IL, z = 0, IL >= 0
   a__take(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   a__uLength(z, z') -{ 2 }-> 1 + a__length(a__zeros) :|: z = 2, z' = 3
   a__uLength(z, z') -{ 2 }-> 1 + a__length(a__uTake2(mark(X11), X21, X3', X4')) :|: z = 2, X3' >= 0, X4' >= 0, X11 >= 0, X21 >= 0, z' = 1 + X11 + X21 + X3' + X4'
   a__uLength(z, z') -{ 2 }-> 1 + a__length(a__uTake1(mark(X7))) :|: z = 2, X7 >= 0, z' = 1 + X7
   a__uLength(z, z') -{ 2 }-> 1 + a__length(a__uLength(mark(X12), X22)) :|: z = 2, z' = 1 + X12 + X22, X12 >= 0, X22 >= 0
   a__uLength(z, z') -{ 2 }-> 1 + a__length(a__take(mark(X1''), mark(X2''))) :|: z = 2, z' = 1 + X1'' + X2'', X1'' >= 0, X2'' >= 0
   a__uLength(z, z') -{ 2 }-> 1 + a__length(a__length(mark(X6))) :|: z = 2, X6 >= 0, z' = 1 + X6
   a__uLength(z, z') -{ 2 }-> 1 + a__length(a__isNatList(X'')) :|: z = 2, z' = 1 + X'', X'' >= 0
   a__uLength(z, z') -{ 2 }-> 1 + a__length(a__isNatIList(X')) :|: z = 2, X' >= 0, z' = 1 + X'
   a__uLength(z, z') -{ 2 }-> 1 + a__length(a__isNat(X5)) :|: z = 2, X5 >= 0, z' = 1 + X5
   a__uLength(z, z') -{ 2 }-> 1 + a__length(a__and(mark(X1'), mark(X2'))) :|: z = 2, z' = 1 + X1' + X2', X2' >= 0, X1' >= 0
   a__uLength(z, z') -{ 2 }-> 1 + a__length(2) :|: z = 2, z' = 2
   a__uLength(z, z') -{ 2 }-> 1 + a__length(1) :|: z = 2, z' = 1
   a__uLength(z, z') -{ 2 }-> 1 + a__length(0) :|: z = 2, z' = 0
   a__uLength(z, z') -{ 2 }-> 1 + a__length(1 + mark(X8)) :|: z = 2, X8 >= 0, z' = 1 + X8
   a__uLength(z, z') -{ 2 }-> 1 + a__length(1 + mark(X13) + X23) :|: z = 2, X13 >= 0, X23 >= 0, z' = 1 + X13 + X23
   a__uLength(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   a__uTake1(z) -{ 1 }-> 1 :|: z = 2
   a__uTake1(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__uTake2(z, z', z'', z1) -{ 1 }-> 1 + mark(N) + (1 + M + IL) :|: z = 2, z' = M, z1 = IL, z'' = N, M >= 0, IL >= 0, N >= 0
   a__uTake2(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__zeros -{ 1 }-> 3 :|: 
   a__zeros -{ 1 }-> 1 + 0 + 3 :|: 
   mark(z) -{ 1 }-> a__zeros :|: z = 3
   mark(z) -{ 2 }-> a__uTake2(a__zeros, X2, X3, X4) :|: X3 >= 0, z = 1 + 3 + X2 + X3 + X4, X2 >= 0, X4 >= 0
   mark(z) -{ 2 }-> a__uTake2(a__uTake2(mark(X1192), X2181, X3104, X457), X2, X3, X4) :|: z = 1 + (1 + X1192 + X2181 + X3104 + X457) + X2 + X3 + X4, X457 >= 0, X2181 >= 0, X3104 >= 0, X3 >= 0, X2 >= 0, X4 >= 0, X1192 >= 0
   mark(z) -{ 2 }-> a__uTake2(a__uTake1(mark(X456)), X2, X3, X4) :|: X456 >= 0, X3 >= 0, z = 1 + (1 + X456) + X2 + X3 + X4, X2 >= 0, X4 >= 0
   mark(z) -{ 2 }-> a__uTake2(a__uLength(mark(X1193), X2182), X2, X3, X4) :|: z = 1 + (1 + X1193 + X2182) + X2 + X3 + X4, X2182 >= 0, X3 >= 0, X1193 >= 0, X2 >= 0, X4 >= 0
   mark(z) -{ 2 }-> a__uTake2(a__take(mark(X1191), mark(X2180)), X2, X3, X4) :|: X1191 >= 0, z = 1 + (1 + X1191 + X2180) + X2 + X3 + X4, X3 >= 0, X2180 >= 0, X2 >= 0, X4 >= 0
   mark(z) -{ 2 }-> a__uTake2(a__length(mark(X455)), X2, X3, X4) :|: z = 1 + (1 + X455) + X2 + X3 + X4, X3 >= 0, X2 >= 0, X4 >= 0, X455 >= 0
   mark(z) -{ 2 }-> a__uTake2(a__isNatList(X453), X2, X3, X4) :|: z = 1 + (1 + X453) + X2 + X3 + X4, X453 >= 0, X3 >= 0, X2 >= 0, X4 >= 0
   mark(z) -{ 2 }-> a__uTake2(a__isNatIList(X452), X2, X3, X4) :|: X452 >= 0, X3 >= 0, z = 1 + (1 + X452) + X2 + X3 + X4, X2 >= 0, X4 >= 0
   mark(z) -{ 2 }-> a__uTake2(a__isNat(X454), X2, X3, X4) :|: X3 >= 0, z = 1 + (1 + X454) + X2 + X3 + X4, X454 >= 0, X2 >= 0, X4 >= 0
   mark(z) -{ 2 }-> a__uTake2(a__and(mark(X1190), mark(X2179)), X2, X3, X4) :|: z = 1 + (1 + X1190 + X2179) + X2 + X3 + X4, X1190 >= 0, X2179 >= 0, X3 >= 0, X2 >= 0, X4 >= 0
   mark(z) -{ 2 }-> a__uTake2(2, X2, X3, X4) :|: X3 >= 0, X2 >= 0, X4 >= 0, z = 1 + 2 + X2 + X3 + X4
   mark(z) -{ 2 }-> a__uTake2(1, X2, X3, X4) :|: X3 >= 0, X2 >= 0, X4 >= 0, z = 1 + 1 + X2 + X3 + X4
   mark(z) -{ 2 }-> a__uTake2(0, X2, X3, X4) :|: X3 >= 0, z = 1 + 0 + X2 + X3 + X4, X2 >= 0, X4 >= 0
   mark(z) -{ 2 }-> a__uTake2(1 + mark(X458), X2, X3, X4) :|: X3 >= 0, z = 1 + (1 + X458) + X2 + X3 + X4, X458 >= 0, X2 >= 0, X4 >= 0
   mark(z) -{ 2 }-> a__uTake2(1 + mark(X1194) + X2183, X2, X3, X4) :|: X1194 >= 0, X2183 >= 0, z = 1 + (1 + X1194 + X2183) + X2 + X3 + X4, X3 >= 0, X2 >= 0, X4 >= 0
   mark(z) -{ 2 }-> a__uTake1(a__zeros) :|: z = 1 + 3
   mark(z) -{ 2 }-> a__uTake1(a__uTake2(mark(X1187), X2176, X3103, X450)) :|: X2176 >= 0, X1187 >= 0, X3103 >= 0, z = 1 + (1 + X1187 + X2176 + X3103 + X450), X450 >= 0
   mark(z) -{ 2 }-> a__uTake1(a__uTake1(mark(X449))) :|: X449 >= 0, z = 1 + (1 + X449)
   mark(z) -{ 2 }-> a__uTake1(a__uLength(mark(X1188), X2177)) :|: X1188 >= 0, X2177 >= 0, z = 1 + (1 + X1188 + X2177)
   mark(z) -{ 2 }-> a__uTake1(a__take(mark(X1186), mark(X2175))) :|: X1186 >= 0, z = 1 + (1 + X1186 + X2175), X2175 >= 0
   mark(z) -{ 2 }-> a__uTake1(a__length(mark(X448))) :|: z = 1 + (1 + X448), X448 >= 0
   mark(z) -{ 2 }-> a__uTake1(a__isNatList(X446)) :|: X446 >= 0, z = 1 + (1 + X446)
   mark(z) -{ 2 }-> a__uTake1(a__isNatIList(X445)) :|: z = 1 + (1 + X445), X445 >= 0
   mark(z) -{ 2 }-> a__uTake1(a__isNat(X447)) :|: z = 1 + (1 + X447), X447 >= 0
   mark(z) -{ 2 }-> a__uTake1(a__and(mark(X1185), mark(X2174))) :|: X1185 >= 0, z = 1 + (1 + X1185 + X2174), X2174 >= 0
   mark(z) -{ 2 }-> a__uTake1(2) :|: z = 1 + 2
   mark(z) -{ 2 }-> a__uTake1(1) :|: z = 1 + 1
   mark(z) -{ 2 }-> a__uTake1(0) :|: z = 1 + 0
   mark(z) -{ 2 }-> a__uTake1(1 + mark(X451)) :|: X451 >= 0, z = 1 + (1 + X451)
   mark(z) -{ 2 }-> a__uTake1(1 + mark(X1189) + X2178) :|: X2178 >= 0, X1189 >= 0, z = 1 + (1 + X1189 + X2178)
   mark(z) -{ 2 }-> a__uLength(a__zeros, X2) :|: X2 >= 0, z = 1 + 3 + X2
   mark(z) -{ 2 }-> a__uLength(a__uTake2(mark(X1197), X2186, X3105, X464), X2) :|: X2186 >= 0, X3105 >= 0, X1197 >= 0, X2 >= 0, z = 1 + (1 + X1197 + X2186 + X3105 + X464) + X2, X464 >= 0
   mark(z) -{ 2 }-> a__uLength(a__uTake1(mark(X463)), X2) :|: X463 >= 0, z = 1 + (1 + X463) + X2, X2 >= 0
   mark(z) -{ 2 }-> a__uLength(a__uLength(mark(X1198), X2187), X2) :|: X1198 >= 0, X2187 >= 0, z = 1 + (1 + X1198 + X2187) + X2, X2 >= 0
   mark(z) -{ 2 }-> a__uLength(a__take(mark(X1196), mark(X2185)), X2) :|: X1196 >= 0, X2 >= 0, z = 1 + (1 + X1196 + X2185) + X2, X2185 >= 0
   mark(z) -{ 2 }-> a__uLength(a__length(mark(X462)), X2) :|: z = 1 + (1 + X462) + X2, X462 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__uLength(a__isNatList(X460), X2) :|: X460 >= 0, z = 1 + (1 + X460) + X2, X2 >= 0
   mark(z) -{ 2 }-> a__uLength(a__isNatIList(X459), X2) :|: z = 1 + (1 + X459) + X2, X459 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__uLength(a__isNat(X461), X2) :|: X461 >= 0, z = 1 + (1 + X461) + X2, X2 >= 0
   mark(z) -{ 2 }-> a__uLength(a__and(mark(X1195), mark(X2184)), X2) :|: X1195 >= 0, X2184 >= 0, X2 >= 0, z = 1 + (1 + X1195 + X2184) + X2
   mark(z) -{ 2 }-> a__uLength(2, X2) :|: z = 1 + 2 + X2, X2 >= 0
   mark(z) -{ 2 }-> a__uLength(1, X2) :|: z = 1 + 1 + X2, X2 >= 0
   mark(z) -{ 2 }-> a__uLength(0, X2) :|: z = 1 + 0 + X2, X2 >= 0
   mark(z) -{ 2 }-> a__uLength(1 + mark(X465), X2) :|: X2 >= 0, z = 1 + (1 + X465) + X2, X465 >= 0
   mark(z) -{ 2 }-> a__uLength(1 + mark(X1199) + X2188, X2) :|: z = 1 + (1 + X1199 + X2188) + X2, X2188 >= 0, X2 >= 0, X1199 >= 0
   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__uTake2(mark(X1102), X286, X324, X423)) :|: X286 >= 0, X324 >= 0, X423 >= 0, z = 1 + (1 + X1102 + X286 + X324 + X423), X1102 >= 0
   mark(z) -{ 2 }-> a__length(a__uTake1(mark(X204))) :|: z = 1 + (1 + X204), X204 >= 0
   mark(z) -{ 2 }-> a__length(a__uLength(mark(X1103), X287)) :|: z = 1 + (1 + X1103 + X287), X287 >= 0, X1103 >= 0
   mark(z) -{ 2 }-> a__length(a__take(mark(X1101), mark(X285))) :|: X1101 >= 0, z = 1 + (1 + X1101 + X285), X285 >= 0
   mark(z) -{ 2 }-> a__length(a__length(mark(X203))) :|: z = 1 + (1 + X203), X203 >= 0
   mark(z) -{ 2 }-> a__length(a__isNatList(X201)) :|: X201 >= 0, z = 1 + (1 + X201)
   mark(z) -{ 2 }-> a__length(a__isNatIList(X200)) :|: z = 1 + (1 + X200), X200 >= 0
   mark(z) -{ 2 }-> a__length(a__isNat(X202)) :|: X202 >= 0, z = 1 + (1 + X202)
   mark(z) -{ 2 }-> a__length(a__and(mark(X1100), mark(X284))) :|: X1100 >= 0, X284 >= 0, z = 1 + (1 + X1100 + X284)
   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(X205)) :|: z = 1 + (1 + X205), X205 >= 0
   mark(z) -{ 2 }-> a__length(1 + mark(X1104) + X288) :|: z = 1 + (1 + X1104 + X288), X1104 >= 0, X288 >= 0
   mark(z) -{ 1 }-> a__isNatList(X) :|: z = 1 + X, X >= 0
   mark(z) -{ 1 }-> a__isNatIList(X) :|: z = 1 + X, X >= 0
   mark(z) -{ 1 }-> a__isNat(X) :|: z = 1 + X, X >= 0
   mark(z) -{ 1 }-> a__and(mark(X1), mark(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


----------------------------------------

(37) 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 :|: 
   a__uTake1(z) -{ 1 }-> 1 :|: z = 2
   a__uTake1(z) -{ 1 }-> 1 + X :|: X >= 0, z = X

----------------------------------------

(38)
Obligation:
Complexity RNTS consisting of the following rules:

   a__and(z, z') -{ 1 }-> mark(T) :|: z = 2, z' = T, T >= 0
   a__and(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   a__isNat(z) -{ 1 }-> a__isNatList(L) :|: z = 1 + L, L >= 0
   a__isNat(z) -{ 1 }-> a__isNat(N) :|: z = 1 + N, N >= 0
   a__isNat(z) -{ 1 }-> 2 :|: z = 0
   a__isNat(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__isNatIList(z) -{ 1 }-> a__isNatList(IL) :|: z = IL, IL >= 0
   a__isNatIList(z) -{ 3 }-> a__and(a__isNatList(L'), a__isNatList(IL)) :|: L' >= 0, z = 1 + (1 + L') + IL, IL >= 0
   a__isNatIList(z) -{ 3 }-> a__and(a__isNatList(L'), a__and(a__isNat(N2), a__isNatIList(IL1))) :|: L' >= 0, IL1 >= 0, z = 1 + (1 + L') + (1 + N2 + IL1), N2 >= 0
   a__isNatIList(z) -{ 3 }-> a__and(a__isNatList(L'), 2) :|: L' >= 0, z = 1 + (1 + L') + 3
   a__isNatIList(z) -{ 3 }-> a__and(a__isNatList(L'), 1 + IL) :|: L' >= 0, z = 1 + (1 + L') + IL, IL >= 0
   a__isNatIList(z) -{ 3 }-> a__and(a__isNat(N'), a__isNatList(IL)) :|: N' >= 0, z = 1 + (1 + N') + IL, IL >= 0
   a__isNatIList(z) -{ 3 }-> a__and(a__isNat(N'), a__and(a__isNat(N1), a__isNatIList(IL''))) :|: IL'' >= 0, N1 >= 0, z = 1 + (1 + N') + (1 + N1 + IL''), N' >= 0
   a__isNatIList(z) -{ 3 }-> a__and(a__isNat(N'), 2) :|: z = 1 + (1 + N') + 3, N' >= 0
   a__isNatIList(z) -{ 3 }-> a__and(a__isNat(N'), 1 + IL) :|: N' >= 0, z = 1 + (1 + N') + IL, IL >= 0
   a__isNatIList(z) -{ 3 }-> a__and(2, a__isNatList(IL)) :|: z = 1 + 0 + IL, IL >= 0
   a__isNatIList(z) -{ 3 }-> a__and(2, a__and(a__isNat(N''), a__isNatIList(IL'))) :|: IL' >= 0, z = 1 + 0 + (1 + N'' + IL'), N'' >= 0
   a__isNatIList(z) -{ 3 }-> a__and(2, 2) :|: z = 1 + 0 + 3
   a__isNatIList(z) -{ 3 }-> a__and(2, 1 + IL) :|: z = 1 + 0 + IL, IL >= 0
   a__isNatIList(z) -{ 3 }-> a__and(1 + N, a__isNatList(IL)) :|: z = 1 + N + IL, IL >= 0, N >= 0
   a__isNatIList(z) -{ 3 }-> a__and(1 + N, a__and(a__isNat(N3), a__isNatIList(IL2))) :|: IL2 >= 0, N3 >= 0, z = 1 + N + (1 + N3 + IL2), N >= 0
   a__isNatIList(z) -{ 3 }-> a__and(1 + N, 2) :|: z = 1 + N + 3, N >= 0
   a__isNatIList(z) -{ 3 }-> a__and(1 + N, 1 + IL) :|: z = 1 + N + IL, IL >= 0, N >= 0
   a__isNatIList(z) -{ 1 }-> 2 :|: z = 3
   a__isNatIList(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__isNatList(z) -{ 3 }-> a__and(a__isNatList(L''), a__and(a__isNat(N10), a__isNatIList(IL5))) :|: L'' >= 0, z = 1 + (1 + L'') + (1 + N10 + IL5), N10 >= 0, IL5 >= 0
   a__isNatList(z) -{ 3 }-> a__and(a__isNatList(L''), a__and(a__isNat(N9), a__isNatList(L3))) :|: L3 >= 0, z = 1 + (1 + L'') + (1 + N9 + L3), N9 >= 0, L'' >= 0
   a__isNatList(z) -{ 3 }-> a__and(a__isNatList(L''), 2) :|: z = 1 + (1 + L'') + 1, L'' >= 0
   a__isNatList(z) -{ 3 }-> a__and(a__isNatList(L''), 1 + L) :|: z = 1 + (1 + L'') + L, L'' >= 0, L >= 0
   a__isNatList(z) -{ 3 }-> a__and(a__isNatList(L5), a__isNatList(IL)) :|: z = 1 + (1 + L5) + IL, L5 >= 0, IL >= 0
   a__isNatList(z) -{ 3 }-> a__and(a__isNatList(L5), a__and(a__isNat(N16), a__isNatIList(IL9))) :|: IL9 >= 0, L5 >= 0, N16 >= 0, z = 1 + (1 + L5) + (1 + N16 + IL9)
   a__isNatList(z) -{ 3 }-> a__and(a__isNatList(L5), 2) :|: L5 >= 0, z = 1 + (1 + L5) + 3
   a__isNatList(z) -{ 3 }-> a__and(a__isNatList(L5), 1 + IL) :|: z = 1 + (1 + L5) + IL, L5 >= 0, IL >= 0
   a__isNatList(z) -{ 3 }-> a__and(a__isNat(N13), a__isNatList(IL)) :|: z = 1 + (1 + N13) + IL, N13 >= 0, IL >= 0
   a__isNatList(z) -{ 3 }-> a__and(a__isNat(N13), a__and(a__isNat(N15), a__isNatIList(IL8))) :|: N15 >= 0, z = 1 + (1 + N13) + (1 + N15 + IL8), IL8 >= 0, N13 >= 0
   a__isNatList(z) -{ 3 }-> a__and(a__isNat(N13), 2) :|: z = 1 + (1 + N13) + 3, N13 >= 0
   a__isNatList(z) -{ 3 }-> a__and(a__isNat(N13), 1 + IL) :|: z = 1 + (1 + N13) + IL, N13 >= 0, IL >= 0
   a__isNatList(z) -{ 3 }-> a__and(a__isNat(N4), a__and(a__isNat(N7), a__isNatList(L2))) :|: z = 1 + (1 + N4) + (1 + N7 + L2), N7 >= 0, L2 >= 0, N4 >= 0
   a__isNatList(z) -{ 3 }-> a__and(a__isNat(N4), a__and(a__isNat(N8), a__isNatIList(IL4))) :|: z = 1 + (1 + N4) + (1 + N8 + IL4), N8 >= 0, IL4 >= 0, N4 >= 0
   a__isNatList(z) -{ 3 }-> a__and(a__isNat(N4), 2) :|: z = 1 + (1 + N4) + 1, N4 >= 0
   a__isNatList(z) -{ 3 }-> a__and(a__isNat(N4), 1 + L) :|: z = 1 + (1 + N4) + L, L >= 0, N4 >= 0
   a__isNatList(z) -{ 3 }-> a__and(2, a__isNatList(IL)) :|: z = 1 + 0 + IL, IL >= 0
   a__isNatList(z) -{ 3 }-> a__and(2, a__and(a__isNat(N14), a__isNatIList(IL7))) :|: IL7 >= 0, N14 >= 0, z = 1 + 0 + (1 + N14 + IL7)
   a__isNatList(z) -{ 3 }-> a__and(2, a__and(a__isNat(N5), a__isNatList(L1))) :|: z = 1 + 0 + (1 + N5 + L1), L1 >= 0, N5 >= 0
   a__isNatList(z) -{ 3 }-> a__and(2, a__and(a__isNat(N6), a__isNatIList(IL3))) :|: IL3 >= 0, z = 1 + 0 + (1 + N6 + IL3), N6 >= 0
   a__isNatList(z) -{ 3 }-> a__and(2, 2) :|: z = 1 + 0 + 1
   a__isNatList(z) -{ 3 }-> a__and(2, 2) :|: z = 1 + 0 + 3
   a__isNatList(z) -{ 3 }-> a__and(2, 1 + IL) :|: z = 1 + 0 + IL, IL >= 0
   a__isNatList(z) -{ 3 }-> a__and(2, 1 + L) :|: z = 1 + 0 + L, L >= 0
   a__isNatList(z) -{ 3 }-> a__and(1 + N, a__isNatList(IL)) :|: z = 1 + N + IL, IL >= 0, N >= 0
   a__isNatList(z) -{ 3 }-> a__and(1 + N, a__and(a__isNat(N11), a__isNatList(L4))) :|: N11 >= 0, z = 1 + N + (1 + N11 + L4), N >= 0, L4 >= 0
   a__isNatList(z) -{ 3 }-> a__and(1 + N, a__and(a__isNat(N12), a__isNatIList(IL6))) :|: z = 1 + N + (1 + N12 + IL6), N12 >= 0, IL6 >= 0, N >= 0
   a__isNatList(z) -{ 3 }-> a__and(1 + N, a__and(a__isNat(N17), a__isNatIList(IL10))) :|: z = 1 + N + (1 + N17 + IL10), IL10 >= 0, N17 >= 0, N >= 0
   a__isNatList(z) -{ 3 }-> a__and(1 + N, 2) :|: z = 1 + N + 1, N >= 0
   a__isNatList(z) -{ 3 }-> a__and(1 + N, 2) :|: z = 1 + N + 3, N >= 0
   a__isNatList(z) -{ 3 }-> a__and(1 + N, 1 + IL) :|: z = 1 + N + IL, IL >= 0, N >= 0
   a__isNatList(z) -{ 3 }-> a__and(1 + N, 1 + L) :|: z = 1 + N + L, L >= 0, N >= 0
   a__isNatList(z) -{ 1 }-> 2 :|: z = 1
   a__isNatList(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__length(z) -{ 3 }-> a__uLength(a__and(a__isNatList(L11), a__and(a__isNat(N45), a__isNatList(L14))), 1 + N45 + L14) :|: z = 1 + (1 + L11) + (1 + N45 + L14), N45 >= 0, L11 >= 0, L14 >= 0
   a__length(z) -{ 3 }-> a__uLength(a__and(a__isNatList(L11), a__and(a__isNat(N46), a__isNatIList(IL30))), 1 + N46 + IL30) :|: N46 >= 0, IL30 >= 0, L11 >= 0, z = 1 + (1 + L11) + (1 + N46 + IL30)
   a__length(z) -{ 3 }-> a__uLength(a__and(a__isNatList(L11), 2), 1) :|: z = 1 + (1 + L11) + 1, L11 >= 0
   a__length(z) -{ 3 }-> a__uLength(a__and(a__isNatList(L11), 1 + L), L) :|: z = 1 + (1 + L11) + L, L11 >= 0, L >= 0
   a__length(z) -{ 3 }-> a__uLength(a__and(a__isNat(N40), a__and(a__isNat(N43), a__isNatList(L13))), 1 + N43 + L13) :|: L13 >= 0, N43 >= 0, z = 1 + (1 + N40) + (1 + N43 + L13), N40 >= 0
   a__length(z) -{ 3 }-> a__uLength(a__and(a__isNat(N40), a__and(a__isNat(N44), a__isNatIList(IL29))), 1 + N44 + IL29) :|: IL29 >= 0, z = 1 + (1 + N40) + (1 + N44 + IL29), N44 >= 0, N40 >= 0
   a__length(z) -{ 3 }-> a__uLength(a__and(a__isNat(N40), 2), 1) :|: z = 1 + (1 + N40) + 1, N40 >= 0
   a__length(z) -{ 3 }-> a__uLength(a__and(a__isNat(N40), 1 + L), L) :|: z = 1 + (1 + N40) + L, L >= 0, N40 >= 0
   a__length(z) -{ 3 }-> a__uLength(a__and(2, a__and(a__isNat(N41), a__isNatList(L12))), 1 + N41 + L12) :|: z = 1 + 0 + (1 + N41 + L12), L12 >= 0, N41 >= 0
   a__length(z) -{ 3 }-> a__uLength(a__and(2, a__and(a__isNat(N42), a__isNatIList(IL28))), 1 + N42 + IL28) :|: N42 >= 0, IL28 >= 0, z = 1 + 0 + (1 + N42 + IL28)
   a__length(z) -{ 3 }-> a__uLength(a__and(2, 2), 1) :|: z = 1 + 0 + 1
   a__length(z) -{ 3 }-> a__uLength(a__and(2, 1 + L), L) :|: z = 1 + 0 + L, L >= 0
   a__length(z) -{ 3 }-> a__uLength(a__and(1 + N, a__and(a__isNat(N47), a__isNatList(L15))), 1 + N47 + L15) :|: z = 1 + N + (1 + N47 + L15), L15 >= 0, N47 >= 0, N >= 0
   a__length(z) -{ 3 }-> a__uLength(a__and(1 + N, a__and(a__isNat(N48), a__isNatIList(IL31))), 1 + N48 + IL31) :|: IL31 >= 0, N48 >= 0, z = 1 + N + (1 + N48 + IL31), N >= 0
   a__length(z) -{ 3 }-> a__uLength(a__and(1 + N, 2), 1) :|: z = 1 + N + 1, N >= 0
   a__length(z) -{ 3 }-> a__uLength(a__and(1 + N, 1 + L), L) :|: z = 1 + N + L, L >= 0, N >= 0
   a__length(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__take(z, z') -{ 1 }-> a__uTake2(a__and(a__isNat(M), a__and(a__isNat(N), a__isNatIList(IL))), M, N, IL) :|: z = 1 + M, M >= 0, IL >= 0, z' = 1 + N + IL, N >= 0
   a__take(z, z') -{ 2 }-> a__uTake1(a__isNatList(IL)) :|: z' = IL, z = 0, IL >= 0
   a__take(z, z') -{ 2 }-> a__uTake1(a__and(a__isNat(N18), a__isNatIList(IL11))) :|: IL11 >= 0, z' = 1 + N18 + IL11, z = 0, N18 >= 0
   a__take(z, z') -{ 3 }-> 1 :|: z' = 3, z = 0, 2 = 2
   a__take(z, z') -{ 3 }-> 1 :|: z' = IL, z = 0, IL >= 0, 1 + IL = 2
   a__take(z, z') -{ 3 }-> 1 + X :|: z' = 3, z = 0, X >= 0, 2 = X
   a__take(z, z') -{ 3 }-> 1 + X :|: z' = IL, z = 0, IL >= 0, X >= 0, 1 + IL = X
   a__take(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   a__uLength(z, z') -{ 2 }-> 1 + a__length(a__uTake2(mark(X11), X21, X3', X4')) :|: z = 2, X3' >= 0, X4' >= 0, X11 >= 0, X21 >= 0, z' = 1 + X11 + X21 + X3' + X4'
   a__uLength(z, z') -{ 2 }-> 1 + a__length(a__uTake1(mark(X7))) :|: z = 2, X7 >= 0, z' = 1 + X7
   a__uLength(z, z') -{ 2 }-> 1 + a__length(a__uLength(mark(X12), X22)) :|: z = 2, z' = 1 + X12 + X22, X12 >= 0, X22 >= 0
   a__uLength(z, z') -{ 2 }-> 1 + a__length(a__take(mark(X1''), mark(X2''))) :|: z = 2, z' = 1 + X1'' + X2'', X1'' >= 0, X2'' >= 0
   a__uLength(z, z') -{ 2 }-> 1 + a__length(a__length(mark(X6))) :|: z = 2, X6 >= 0, z' = 1 + X6
   a__uLength(z, z') -{ 2 }-> 1 + a__length(a__isNatList(X'')) :|: z = 2, z' = 1 + X'', X'' >= 0
   a__uLength(z, z') -{ 2 }-> 1 + a__length(a__isNatIList(X')) :|: z = 2, X' >= 0, z' = 1 + X'
   a__uLength(z, z') -{ 2 }-> 1 + a__length(a__isNat(X5)) :|: z = 2, X5 >= 0, z' = 1 + X5
   a__uLength(z, z') -{ 2 }-> 1 + a__length(a__and(mark(X1'), mark(X2'))) :|: z = 2, z' = 1 + X1' + X2', X2' >= 0, X1' >= 0
   a__uLength(z, z') -{ 3 }-> 1 + a__length(3) :|: z = 2, z' = 3
   a__uLength(z, z') -{ 2 }-> 1 + a__length(2) :|: z = 2, z' = 2
   a__uLength(z, z') -{ 2 }-> 1 + a__length(1) :|: z = 2, z' = 1
   a__uLength(z, z') -{ 2 }-> 1 + a__length(0) :|: z = 2, z' = 0
   a__uLength(z, z') -{ 2 }-> 1 + a__length(1 + mark(X8)) :|: z = 2, X8 >= 0, z' = 1 + X8
   a__uLength(z, z') -{ 2 }-> 1 + a__length(1 + mark(X13) + X23) :|: z = 2, X13 >= 0, X23 >= 0, z' = 1 + X13 + X23
   a__uLength(z, z') -{ 3 }-> 1 + a__length(1 + 0 + 3) :|: z = 2, z' = 3
   a__uLength(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   a__uTake1(z) -{ 1 }-> 1 :|: z = 2
   a__uTake1(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__uTake2(z, z', z'', z1) -{ 1 }-> 1 + mark(N) + (1 + M + IL) :|: z = 2, z' = M, z1 = IL, z'' = N, M >= 0, IL >= 0, N >= 0
   a__uTake2(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__zeros -{ 1 }-> 3 :|: 
   a__zeros -{ 1 }-> 1 + 0 + 3 :|: 
   mark(z) -{ 2 }-> a__uTake2(a__uTake2(mark(X1192), X2181, X3104, X457), X2, X3, X4) :|: z = 1 + (1 + X1192 + X2181 + X3104 + X457) + X2 + X3 + X4, X457 >= 0, X2181 >= 0, X3104 >= 0, X3 >= 0, X2 >= 0, X4 >= 0, X1192 >= 0
   mark(z) -{ 2 }-> a__uTake2(a__uTake1(mark(X456)), X2, X3, X4) :|: X456 >= 0, X3 >= 0, z = 1 + (1 + X456) + X2 + X3 + X4, X2 >= 0, X4 >= 0
   mark(z) -{ 2 }-> a__uTake2(a__uLength(mark(X1193), X2182), X2, X3, X4) :|: z = 1 + (1 + X1193 + X2182) + X2 + X3 + X4, X2182 >= 0, X3 >= 0, X1193 >= 0, X2 >= 0, X4 >= 0
   mark(z) -{ 2 }-> a__uTake2(a__take(mark(X1191), mark(X2180)), X2, X3, X4) :|: X1191 >= 0, z = 1 + (1 + X1191 + X2180) + X2 + X3 + X4, X3 >= 0, X2180 >= 0, X2 >= 0, X4 >= 0
   mark(z) -{ 2 }-> a__uTake2(a__length(mark(X455)), X2, X3, X4) :|: z = 1 + (1 + X455) + X2 + X3 + X4, X3 >= 0, X2 >= 0, X4 >= 0, X455 >= 0
   mark(z) -{ 2 }-> a__uTake2(a__isNatList(X453), X2, X3, X4) :|: z = 1 + (1 + X453) + X2 + X3 + X4, X453 >= 0, X3 >= 0, X2 >= 0, X4 >= 0
   mark(z) -{ 2 }-> a__uTake2(a__isNatIList(X452), X2, X3, X4) :|: X452 >= 0, X3 >= 0, z = 1 + (1 + X452) + X2 + X3 + X4, X2 >= 0, X4 >= 0
   mark(z) -{ 2 }-> a__uTake2(a__isNat(X454), X2, X3, X4) :|: X3 >= 0, z = 1 + (1 + X454) + X2 + X3 + X4, X454 >= 0, X2 >= 0, X4 >= 0
   mark(z) -{ 2 }-> a__uTake2(a__and(mark(X1190), mark(X2179)), X2, X3, X4) :|: z = 1 + (1 + X1190 + X2179) + X2 + X3 + X4, X1190 >= 0, X2179 >= 0, X3 >= 0, X2 >= 0, X4 >= 0
   mark(z) -{ 3 }-> a__uTake2(3, X2, X3, X4) :|: X3 >= 0, z = 1 + 3 + X2 + X3 + X4, X2 >= 0, X4 >= 0
   mark(z) -{ 2 }-> a__uTake2(2, X2, X3, X4) :|: X3 >= 0, X2 >= 0, X4 >= 0, z = 1 + 2 + X2 + X3 + X4
   mark(z) -{ 2 }-> a__uTake2(1, X2, X3, X4) :|: X3 >= 0, X2 >= 0, X4 >= 0, z = 1 + 1 + X2 + X3 + X4
   mark(z) -{ 2 }-> a__uTake2(0, X2, X3, X4) :|: X3 >= 0, z = 1 + 0 + X2 + X3 + X4, X2 >= 0, X4 >= 0
   mark(z) -{ 2 }-> a__uTake2(1 + mark(X458), X2, X3, X4) :|: X3 >= 0, z = 1 + (1 + X458) + X2 + X3 + X4, X458 >= 0, X2 >= 0, X4 >= 0
   mark(z) -{ 2 }-> a__uTake2(1 + mark(X1194) + X2183, X2, X3, X4) :|: X1194 >= 0, X2183 >= 0, z = 1 + (1 + X1194 + X2183) + X2 + X3 + X4, X3 >= 0, X2 >= 0, X4 >= 0
   mark(z) -{ 3 }-> a__uTake2(1 + 0 + 3, X2, X3, X4) :|: X3 >= 0, z = 1 + 3 + X2 + X3 + X4, X2 >= 0, X4 >= 0
   mark(z) -{ 2 }-> a__uTake1(a__uTake2(mark(X1187), X2176, X3103, X450)) :|: X2176 >= 0, X1187 >= 0, X3103 >= 0, z = 1 + (1 + X1187 + X2176 + X3103 + X450), X450 >= 0
   mark(z) -{ 2 }-> a__uTake1(a__uTake1(mark(X449))) :|: X449 >= 0, z = 1 + (1 + X449)
   mark(z) -{ 2 }-> a__uTake1(a__uLength(mark(X1188), X2177)) :|: X1188 >= 0, X2177 >= 0, z = 1 + (1 + X1188 + X2177)
   mark(z) -{ 2 }-> a__uTake1(a__take(mark(X1186), mark(X2175))) :|: X1186 >= 0, z = 1 + (1 + X1186 + X2175), X2175 >= 0
   mark(z) -{ 2 }-> a__uTake1(a__length(mark(X448))) :|: z = 1 + (1 + X448), X448 >= 0
   mark(z) -{ 2 }-> a__uTake1(a__isNatList(X446)) :|: X446 >= 0, z = 1 + (1 + X446)
   mark(z) -{ 2 }-> a__uTake1(a__isNatIList(X445)) :|: z = 1 + (1 + X445), X445 >= 0
   mark(z) -{ 2 }-> a__uTake1(a__isNat(X447)) :|: z = 1 + (1 + X447), X447 >= 0
   mark(z) -{ 2 }-> a__uTake1(a__and(mark(X1185), mark(X2174))) :|: X1185 >= 0, z = 1 + (1 + X1185 + X2174), X2174 >= 0
   mark(z) -{ 2 }-> a__uTake1(1 + mark(X451)) :|: X451 >= 0, z = 1 + (1 + X451)
   mark(z) -{ 2 }-> a__uTake1(1 + mark(X1189) + X2178) :|: X2178 >= 0, X1189 >= 0, z = 1 + (1 + X1189 + X2178)
   mark(z) -{ 2 }-> a__uLength(a__uTake2(mark(X1197), X2186, X3105, X464), X2) :|: X2186 >= 0, X3105 >= 0, X1197 >= 0, X2 >= 0, z = 1 + (1 + X1197 + X2186 + X3105 + X464) + X2, X464 >= 0
   mark(z) -{ 2 }-> a__uLength(a__uTake1(mark(X463)), X2) :|: X463 >= 0, z = 1 + (1 + X463) + X2, X2 >= 0
   mark(z) -{ 2 }-> a__uLength(a__uLength(mark(X1198), X2187), X2) :|: X1198 >= 0, X2187 >= 0, z = 1 + (1 + X1198 + X2187) + X2, X2 >= 0
   mark(z) -{ 2 }-> a__uLength(a__take(mark(X1196), mark(X2185)), X2) :|: X1196 >= 0, X2 >= 0, z = 1 + (1 + X1196 + X2185) + X2, X2185 >= 0
   mark(z) -{ 2 }-> a__uLength(a__length(mark(X462)), X2) :|: z = 1 + (1 + X462) + X2, X462 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__uLength(a__isNatList(X460), X2) :|: X460 >= 0, z = 1 + (1 + X460) + X2, X2 >= 0
   mark(z) -{ 2 }-> a__uLength(a__isNatIList(X459), X2) :|: z = 1 + (1 + X459) + X2, X459 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__uLength(a__isNat(X461), X2) :|: X461 >= 0, z = 1 + (1 + X461) + X2, X2 >= 0
   mark(z) -{ 2 }-> a__uLength(a__and(mark(X1195), mark(X2184)), X2) :|: X1195 >= 0, X2184 >= 0, X2 >= 0, z = 1 + (1 + X1195 + X2184) + X2
   mark(z) -{ 3 }-> a__uLength(3, X2) :|: X2 >= 0, z = 1 + 3 + X2
   mark(z) -{ 2 }-> a__uLength(2, X2) :|: z = 1 + 2 + X2, X2 >= 0
   mark(z) -{ 2 }-> a__uLength(1, X2) :|: z = 1 + 1 + X2, X2 >= 0
   mark(z) -{ 2 }-> a__uLength(0, X2) :|: z = 1 + 0 + X2, X2 >= 0
   mark(z) -{ 2 }-> a__uLength(1 + mark(X465), X2) :|: X2 >= 0, z = 1 + (1 + X465) + X2, X465 >= 0
   mark(z) -{ 2 }-> a__uLength(1 + mark(X1199) + X2188, X2) :|: z = 1 + (1 + X1199 + X2188) + X2, X2188 >= 0, X2 >= 0, X1199 >= 0
   mark(z) -{ 3 }-> a__uLength(1 + 0 + 3, X2) :|: X2 >= 0, z = 1 + 3 + X2
   mark(z) -{ 1 }-> a__take(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   mark(z) -{ 2 }-> a__length(a__uTake2(mark(X1102), X286, X324, X423)) :|: X286 >= 0, X324 >= 0, X423 >= 0, z = 1 + (1 + X1102 + X286 + X324 + X423), X1102 >= 0
   mark(z) -{ 2 }-> a__length(a__uTake1(mark(X204))) :|: z = 1 + (1 + X204), X204 >= 0
   mark(z) -{ 2 }-> a__length(a__uLength(mark(X1103), X287)) :|: z = 1 + (1 + X1103 + X287), X287 >= 0, X1103 >= 0
   mark(z) -{ 2 }-> a__length(a__take(mark(X1101), mark(X285))) :|: X1101 >= 0, z = 1 + (1 + X1101 + X285), X285 >= 0
   mark(z) -{ 2 }-> a__length(a__length(mark(X203))) :|: z = 1 + (1 + X203), X203 >= 0
   mark(z) -{ 2 }-> a__length(a__isNatList(X201)) :|: X201 >= 0, z = 1 + (1 + X201)
   mark(z) -{ 2 }-> a__length(a__isNatIList(X200)) :|: z = 1 + (1 + X200), X200 >= 0
   mark(z) -{ 2 }-> a__length(a__isNat(X202)) :|: X202 >= 0, z = 1 + (1 + X202)
   mark(z) -{ 2 }-> a__length(a__and(mark(X1100), mark(X284))) :|: X1100 >= 0, X284 >= 0, z = 1 + (1 + X1100 + X284)
   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(X205)) :|: z = 1 + (1 + X205), X205 >= 0
   mark(z) -{ 2 }-> a__length(1 + mark(X1104) + X288) :|: z = 1 + (1 + X1104 + X288), X1104 >= 0, X288 >= 0
   mark(z) -{ 3 }-> a__length(1 + 0 + 3) :|: z = 1 + 3
   mark(z) -{ 1 }-> a__isNatList(X) :|: z = 1 + X, X >= 0
   mark(z) -{ 1 }-> a__isNatIList(X) :|: z = 1 + X, X >= 0
   mark(z) -{ 1 }-> a__isNat(X) :|: z = 1 + X, X >= 0
   mark(z) -{ 1 }-> a__and(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   mark(z) -{ 2 }-> 3 :|: z = 3
   mark(z) -{ 1 }-> 2 :|: z = 2
   mark(z) -{ 1 }-> 1 :|: z = 1
   mark(z) -{ 3 }-> 1 :|: z = 1 + 2, 2 = 2
   mark(z) -{ 1 }-> 0 :|: z = 0
   mark(z) -{ 3 }-> 1 + X :|: z = 1 + 2, X >= 0, 2 = X
   mark(z) -{ 3 }-> 1 + X :|: z = 1 + 0, X >= 0, 0 = X
   mark(z) -{ 3 }-> 1 + X :|: z = 1 + 1, X >= 0, 1 = X
   mark(z) -{ 4 }-> 1 + X :|: z = 1 + 3, X >= 0, 3 = X
   mark(z) -{ 4 }-> 1 + X :|: z = 1 + 3, X >= 0, 1 + 0 + 3 = X
   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


----------------------------------------

(39) SimplificationProof (BOTH BOUNDS(ID, ID))
Simplified the RNTS by moving equalities from the constraints into the right-hand sides.
----------------------------------------

(40)
Obligation:
Complexity RNTS consisting of the following rules:

   a__and(z, z') -{ 1 }-> mark(z') :|: z = 2, z' >= 0
   a__and(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   a__isNat(z) -{ 1 }-> a__isNatList(z - 1) :|: z - 1 >= 0
   a__isNat(z) -{ 1 }-> a__isNat(z - 1) :|: z - 1 >= 0
   a__isNat(z) -{ 1 }-> 2 :|: z = 0
   a__isNat(z) -{ 1 }-> 1 + z :|: z >= 0
   a__isNatIList(z) -{ 1 }-> a__isNatList(z) :|: z >= 0
   a__isNatIList(z) -{ 3 }-> a__and(a__isNatList(L'), a__isNatList(IL)) :|: L' >= 0, z = 1 + (1 + L') + IL, IL >= 0
   a__isNatIList(z) -{ 3 }-> a__and(a__isNatList(L'), a__and(a__isNat(N2), a__isNatIList(IL1))) :|: L' >= 0, IL1 >= 0, z = 1 + (1 + L') + (1 + N2 + IL1), N2 >= 0
   a__isNatIList(z) -{ 3 }-> a__and(a__isNatList(L'), 1 + IL) :|: L' >= 0, z = 1 + (1 + L') + IL, IL >= 0
   a__isNatIList(z) -{ 3 }-> a__and(a__isNatList(z - 5), 2) :|: z - 5 >= 0
   a__isNatIList(z) -{ 3 }-> a__and(a__isNat(N'), a__isNatList(IL)) :|: N' >= 0, z = 1 + (1 + N') + IL, IL >= 0
   a__isNatIList(z) -{ 3 }-> a__and(a__isNat(N'), a__and(a__isNat(N1), a__isNatIList(IL''))) :|: IL'' >= 0, N1 >= 0, z = 1 + (1 + N') + (1 + N1 + IL''), N' >= 0
   a__isNatIList(z) -{ 3 }-> a__and(a__isNat(N'), 1 + IL) :|: N' >= 0, z = 1 + (1 + N') + IL, IL >= 0
   a__isNatIList(z) -{ 3 }-> a__and(a__isNat(z - 5), 2) :|: z - 5 >= 0
   a__isNatIList(z) -{ 3 }-> a__and(2, a__isNatList(z - 1)) :|: z - 1 >= 0
   a__isNatIList(z) -{ 3 }-> a__and(2, a__and(a__isNat(N''), a__isNatIList(IL'))) :|: IL' >= 0, z = 1 + 0 + (1 + N'' + IL'), N'' >= 0
   a__isNatIList(z) -{ 3 }-> a__and(2, 2) :|: z = 1 + 0 + 3
   a__isNatIList(z) -{ 3 }-> a__and(2, 1 + (z - 1)) :|: z - 1 >= 0
   a__isNatIList(z) -{ 3 }-> a__and(1 + N, a__isNatList(IL)) :|: z = 1 + N + IL, IL >= 0, N >= 0
   a__isNatIList(z) -{ 3 }-> a__and(1 + N, a__and(a__isNat(N3), a__isNatIList(IL2))) :|: IL2 >= 0, N3 >= 0, z = 1 + N + (1 + N3 + IL2), N >= 0
   a__isNatIList(z) -{ 3 }-> a__and(1 + N, 1 + IL) :|: z = 1 + N + IL, IL >= 0, N >= 0
   a__isNatIList(z) -{ 3 }-> a__and(1 + (z - 4), 2) :|: z - 4 >= 0
   a__isNatIList(z) -{ 1 }-> 2 :|: z = 3
   a__isNatIList(z) -{ 1 }-> 1 + z :|: z >= 0
   a__isNatList(z) -{ 3 }-> a__and(a__isNatList(L''), a__and(a__isNat(N10), a__isNatIList(IL5))) :|: L'' >= 0, z = 1 + (1 + L'') + (1 + N10 + IL5), N10 >= 0, IL5 >= 0
   a__isNatList(z) -{ 3 }-> a__and(a__isNatList(L''), a__and(a__isNat(N9), a__isNatList(L3))) :|: L3 >= 0, z = 1 + (1 + L'') + (1 + N9 + L3), N9 >= 0, L'' >= 0
   a__isNatList(z) -{ 3 }-> a__and(a__isNatList(L''), 1 + L) :|: z = 1 + (1 + L'') + L, L'' >= 0, L >= 0
   a__isNatList(z) -{ 3 }-> a__and(a__isNatList(L5), a__isNatList(IL)) :|: z = 1 + (1 + L5) + IL, L5 >= 0, IL >= 0
   a__isNatList(z) -{ 3 }-> a__and(a__isNatList(L5), a__and(a__isNat(N16), a__isNatIList(IL9))) :|: IL9 >= 0, L5 >= 0, N16 >= 0, z = 1 + (1 + L5) + (1 + N16 + IL9)
   a__isNatList(z) -{ 3 }-> a__and(a__isNatList(L5), 1 + IL) :|: z = 1 + (1 + L5) + IL, L5 >= 0, IL >= 0
   a__isNatList(z) -{ 3 }-> a__and(a__isNatList(z - 5), 2) :|: z - 5 >= 0
   a__isNatList(z) -{ 3 }-> a__and(a__isNatList(z - 3), 2) :|: z - 3 >= 0
   a__isNatList(z) -{ 3 }-> a__and(a__isNat(N13), a__isNatList(IL)) :|: z = 1 + (1 + N13) + IL, N13 >= 0, IL >= 0
   a__isNatList(z) -{ 3 }-> a__and(a__isNat(N13), a__and(a__isNat(N15), a__isNatIList(IL8))) :|: N15 >= 0, z = 1 + (1 + N13) + (1 + N15 + IL8), IL8 >= 0, N13 >= 0
   a__isNatList(z) -{ 3 }-> a__and(a__isNat(N13), 1 + IL) :|: z = 1 + (1 + N13) + IL, N13 >= 0, IL >= 0
   a__isNatList(z) -{ 3 }-> a__and(a__isNat(N4), a__and(a__isNat(N7), a__isNatList(L2))) :|: z = 1 + (1 + N4) + (1 + N7 + L2), N7 >= 0, L2 >= 0, N4 >= 0
   a__isNatList(z) -{ 3 }-> a__and(a__isNat(N4), a__and(a__isNat(N8), a__isNatIList(IL4))) :|: z = 1 + (1 + N4) + (1 + N8 + IL4), N8 >= 0, IL4 >= 0, N4 >= 0
   a__isNatList(z) -{ 3 }-> a__and(a__isNat(N4), 1 + L) :|: z = 1 + (1 + N4) + L, L >= 0, N4 >= 0
   a__isNatList(z) -{ 3 }-> a__and(a__isNat(z - 5), 2) :|: z - 5 >= 0
   a__isNatList(z) -{ 3 }-> a__and(a__isNat(z - 3), 2) :|: z - 3 >= 0
   a__isNatList(z) -{ 3 }-> a__and(2, a__isNatList(z - 1)) :|: z - 1 >= 0
   a__isNatList(z) -{ 3 }-> a__and(2, a__and(a__isNat(N14), a__isNatIList(IL7))) :|: IL7 >= 0, N14 >= 0, z = 1 + 0 + (1 + N14 + IL7)
   a__isNatList(z) -{ 3 }-> a__and(2, a__and(a__isNat(N5), a__isNatList(L1))) :|: z = 1 + 0 + (1 + N5 + L1), L1 >= 0, N5 >= 0
   a__isNatList(z) -{ 3 }-> a__and(2, a__and(a__isNat(N6), a__isNatIList(IL3))) :|: IL3 >= 0, z = 1 + 0 + (1 + N6 + IL3), N6 >= 0
   a__isNatList(z) -{ 3 }-> a__and(2, 2) :|: z = 1 + 0 + 1
   a__isNatList(z) -{ 3 }-> a__and(2, 2) :|: z = 1 + 0 + 3
   a__isNatList(z) -{ 3 }-> a__and(2, 1 + (z - 1)) :|: z - 1 >= 0
   a__isNatList(z) -{ 3 }-> a__and(1 + N, a__isNatList(IL)) :|: z = 1 + N + IL, IL >= 0, N >= 0
   a__isNatList(z) -{ 3 }-> a__and(1 + N, a__and(a__isNat(N11), a__isNatList(L4))) :|: N11 >= 0, z = 1 + N + (1 + N11 + L4), N >= 0, L4 >= 0
   a__isNatList(z) -{ 3 }-> a__and(1 + N, a__and(a__isNat(N12), a__isNatIList(IL6))) :|: z = 1 + N + (1 + N12 + IL6), N12 >= 0, IL6 >= 0, N >= 0
   a__isNatList(z) -{ 3 }-> a__and(1 + N, a__and(a__isNat(N17), a__isNatIList(IL10))) :|: z = 1 + N + (1 + N17 + IL10), IL10 >= 0, N17 >= 0, N >= 0
   a__isNatList(z) -{ 3 }-> a__and(1 + N, 1 + IL) :|: z = 1 + N + IL, IL >= 0, N >= 0
   a__isNatList(z) -{ 3 }-> a__and(1 + N, 1 + L) :|: z = 1 + N + L, L >= 0, N >= 0
   a__isNatList(z) -{ 3 }-> a__and(1 + (z - 4), 2) :|: z - 4 >= 0
   a__isNatList(z) -{ 3 }-> a__and(1 + (z - 2), 2) :|: z - 2 >= 0
   a__isNatList(z) -{ 1 }-> 2 :|: z = 1
   a__isNatList(z) -{ 1 }-> 1 + z :|: z >= 0
   a__length(z) -{ 3 }-> a__uLength(a__and(a__isNatList(L11), a__and(a__isNat(N45), a__isNatList(L14))), 1 + N45 + L14) :|: z = 1 + (1 + L11) + (1 + N45 + L14), N45 >= 0, L11 >= 0, L14 >= 0
   a__length(z) -{ 3 }-> a__uLength(a__and(a__isNatList(L11), a__and(a__isNat(N46), a__isNatIList(IL30))), 1 + N46 + IL30) :|: N46 >= 0, IL30 >= 0, L11 >= 0, z = 1 + (1 + L11) + (1 + N46 + IL30)
   a__length(z) -{ 3 }-> a__uLength(a__and(a__isNatList(L11), 1 + L), L) :|: z = 1 + (1 + L11) + L, L11 >= 0, L >= 0
   a__length(z) -{ 3 }-> a__uLength(a__and(a__isNatList(z - 3), 2), 1) :|: z - 3 >= 0
   a__length(z) -{ 3 }-> a__uLength(a__and(a__isNat(N40), a__and(a__isNat(N43), a__isNatList(L13))), 1 + N43 + L13) :|: L13 >= 0, N43 >= 0, z = 1 + (1 + N40) + (1 + N43 + L13), N40 >= 0
   a__length(z) -{ 3 }-> a__uLength(a__and(a__isNat(N40), a__and(a__isNat(N44), a__isNatIList(IL29))), 1 + N44 + IL29) :|: IL29 >= 0, z = 1 + (1 + N40) + (1 + N44 + IL29), N44 >= 0, N40 >= 0
   a__length(z) -{ 3 }-> a__uLength(a__and(a__isNat(N40), 1 + L), L) :|: z = 1 + (1 + N40) + L, L >= 0, N40 >= 0
   a__length(z) -{ 3 }-> a__uLength(a__and(a__isNat(z - 3), 2), 1) :|: z - 3 >= 0
   a__length(z) -{ 3 }-> a__uLength(a__and(2, a__and(a__isNat(N41), a__isNatList(L12))), 1 + N41 + L12) :|: z = 1 + 0 + (1 + N41 + L12), L12 >= 0, N41 >= 0
   a__length(z) -{ 3 }-> a__uLength(a__and(2, a__and(a__isNat(N42), a__isNatIList(IL28))), 1 + N42 + IL28) :|: N42 >= 0, IL28 >= 0, z = 1 + 0 + (1 + N42 + IL28)
   a__length(z) -{ 3 }-> a__uLength(a__and(2, 2), 1) :|: z = 1 + 0 + 1
   a__length(z) -{ 3 }-> a__uLength(a__and(2, 1 + (z - 1)), z - 1) :|: z - 1 >= 0
   a__length(z) -{ 3 }-> a__uLength(a__and(1 + N, a__and(a__isNat(N47), a__isNatList(L15))), 1 + N47 + L15) :|: z = 1 + N + (1 + N47 + L15), L15 >= 0, N47 >= 0, N >= 0
   a__length(z) -{ 3 }-> a__uLength(a__and(1 + N, a__and(a__isNat(N48), a__isNatIList(IL31))), 1 + N48 + IL31) :|: IL31 >= 0, N48 >= 0, z = 1 + N + (1 + N48 + IL31), N >= 0
   a__length(z) -{ 3 }-> a__uLength(a__and(1 + N, 1 + L), L) :|: z = 1 + N + L, L >= 0, N >= 0
   a__length(z) -{ 3 }-> a__uLength(a__and(1 + (z - 2), 2), 1) :|: z - 2 >= 0
   a__length(z) -{ 1 }-> 1 + z :|: z >= 0
   a__take(z, z') -{ 1 }-> a__uTake2(a__and(a__isNat(z - 1), a__and(a__isNat(N), a__isNatIList(IL))), z - 1, N, IL) :|: z - 1 >= 0, IL >= 0, z' = 1 + N + IL, N >= 0
   a__take(z, z') -{ 2 }-> a__uTake1(a__isNatList(z')) :|: z = 0, z' >= 0
   a__take(z, z') -{ 2 }-> a__uTake1(a__and(a__isNat(N18), a__isNatIList(IL11))) :|: IL11 >= 0, z' = 1 + N18 + IL11, z = 0, N18 >= 0
   a__take(z, z') -{ 3 }-> 1 :|: z' = 3, z = 0, 2 = 2
   a__take(z, z') -{ 3 }-> 1 :|: z = 0, z' >= 0, 1 + z' = 2
   a__take(z, z') -{ 3 }-> 1 + X :|: z' = 3, z = 0, X >= 0, 2 = X
   a__take(z, z') -{ 3 }-> 1 + X :|: z = 0, z' >= 0, X >= 0, 1 + z' = X
   a__take(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   a__uLength(z, z') -{ 2 }-> 1 + a__length(a__uTake2(mark(X11), X21, X3', X4')) :|: z = 2, X3' >= 0, X4' >= 0, X11 >= 0, X21 >= 0, z' = 1 + X11 + X21 + X3' + X4'
   a__uLength(z, z') -{ 2 }-> 1 + a__length(a__uTake1(mark(z' - 1))) :|: z = 2, z' - 1 >= 0
   a__uLength(z, z') -{ 2 }-> 1 + a__length(a__uLength(mark(X12), X22)) :|: z = 2, z' = 1 + X12 + X22, X12 >= 0, X22 >= 0
   a__uLength(z, z') -{ 2 }-> 1 + a__length(a__take(mark(X1''), mark(X2''))) :|: z = 2, z' = 1 + X1'' + X2'', X1'' >= 0, X2'' >= 0
   a__uLength(z, z') -{ 2 }-> 1 + a__length(a__length(mark(z' - 1))) :|: z = 2, z' - 1 >= 0
   a__uLength(z, z') -{ 2 }-> 1 + a__length(a__isNatList(z' - 1)) :|: z = 2, z' - 1 >= 0
   a__uLength(z, z') -{ 2 }-> 1 + a__length(a__isNatIList(z' - 1)) :|: z = 2, z' - 1 >= 0
   a__uLength(z, z') -{ 2 }-> 1 + a__length(a__isNat(z' - 1)) :|: z = 2, z' - 1 >= 0
   a__uLength(z, z') -{ 2 }-> 1 + a__length(a__and(mark(X1'), mark(X2'))) :|: z = 2, z' = 1 + X1' + X2', X2' >= 0, X1' >= 0
   a__uLength(z, z') -{ 3 }-> 1 + a__length(3) :|: z = 2, z' = 3
   a__uLength(z, z') -{ 2 }-> 1 + a__length(2) :|: z = 2, z' = 2
   a__uLength(z, z') -{ 2 }-> 1 + a__length(1) :|: z = 2, z' = 1
   a__uLength(z, z') -{ 2 }-> 1 + a__length(0) :|: z = 2, z' = 0
   a__uLength(z, z') -{ 2 }-> 1 + a__length(1 + mark(z' - 1)) :|: z = 2, z' - 1 >= 0
   a__uLength(z, z') -{ 2 }-> 1 + a__length(1 + mark(X13) + X23) :|: z = 2, X13 >= 0, X23 >= 0, z' = 1 + X13 + X23
   a__uLength(z, z') -{ 3 }-> 1 + a__length(1 + 0 + 3) :|: z = 2, z' = 3
   a__uLength(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   a__uTake1(z) -{ 1 }-> 1 :|: z = 2
   a__uTake1(z) -{ 1 }-> 1 + z :|: z >= 0
   a__uTake2(z, z', z'', z1) -{ 1 }-> 1 + mark(z'') + (1 + z' + z1) :|: z = 2, z' >= 0, z1 >= 0, z'' >= 0
   a__uTake2(z, z', z'', z1) -{ 1 }-> 1 + z + z' + z'' + z1 :|: z >= 0, z'' >= 0, z' >= 0, z1 >= 0
   a__zeros -{ 1 }-> 3 :|: 
   a__zeros -{ 1 }-> 1 + 0 + 3 :|: 
   mark(z) -{ 2 }-> a__uTake2(a__uTake2(mark(X1192), X2181, X3104, X457), X2, X3, X4) :|: z = 1 + (1 + X1192 + X2181 + X3104 + X457) + X2 + X3 + X4, X457 >= 0, X2181 >= 0, X3104 >= 0, X3 >= 0, X2 >= 0, X4 >= 0, X1192 >= 0
   mark(z) -{ 2 }-> a__uTake2(a__uTake1(mark(X456)), X2, X3, X4) :|: X456 >= 0, X3 >= 0, z = 1 + (1 + X456) + X2 + X3 + X4, X2 >= 0, X4 >= 0
   mark(z) -{ 2 }-> a__uTake2(a__uLength(mark(X1193), X2182), X2, X3, X4) :|: z = 1 + (1 + X1193 + X2182) + X2 + X3 + X4, X2182 >= 0, X3 >= 0, X1193 >= 0, X2 >= 0, X4 >= 0
   mark(z) -{ 2 }-> a__uTake2(a__take(mark(X1191), mark(X2180)), X2, X3, X4) :|: X1191 >= 0, z = 1 + (1 + X1191 + X2180) + X2 + X3 + X4, X3 >= 0, X2180 >= 0, X2 >= 0, X4 >= 0
   mark(z) -{ 2 }-> a__uTake2(a__length(mark(X455)), X2, X3, X4) :|: z = 1 + (1 + X455) + X2 + X3 + X4, X3 >= 0, X2 >= 0, X4 >= 0, X455 >= 0
   mark(z) -{ 2 }-> a__uTake2(a__isNatList(X453), X2, X3, X4) :|: z = 1 + (1 + X453) + X2 + X3 + X4, X453 >= 0, X3 >= 0, X2 >= 0, X4 >= 0
   mark(z) -{ 2 }-> a__uTake2(a__isNatIList(X452), X2, X3, X4) :|: X452 >= 0, X3 >= 0, z = 1 + (1 + X452) + X2 + X3 + X4, X2 >= 0, X4 >= 0
   mark(z) -{ 2 }-> a__uTake2(a__isNat(X454), X2, X3, X4) :|: X3 >= 0, z = 1 + (1 + X454) + X2 + X3 + X4, X454 >= 0, X2 >= 0, X4 >= 0
   mark(z) -{ 2 }-> a__uTake2(a__and(mark(X1190), mark(X2179)), X2, X3, X4) :|: z = 1 + (1 + X1190 + X2179) + X2 + X3 + X4, X1190 >= 0, X2179 >= 0, X3 >= 0, X2 >= 0, X4 >= 0
   mark(z) -{ 3 }-> a__uTake2(3, X2, X3, X4) :|: X3 >= 0, z = 1 + 3 + X2 + X3 + X4, X2 >= 0, X4 >= 0
   mark(z) -{ 2 }-> a__uTake2(2, X2, X3, X4) :|: X3 >= 0, X2 >= 0, X4 >= 0, z = 1 + 2 + X2 + X3 + X4
   mark(z) -{ 2 }-> a__uTake2(1, X2, X3, X4) :|: X3 >= 0, X2 >= 0, X4 >= 0, z = 1 + 1 + X2 + X3 + X4
   mark(z) -{ 2 }-> a__uTake2(0, X2, X3, X4) :|: X3 >= 0, z = 1 + 0 + X2 + X3 + X4, X2 >= 0, X4 >= 0
   mark(z) -{ 2 }-> a__uTake2(1 + mark(X458), X2, X3, X4) :|: X3 >= 0, z = 1 + (1 + X458) + X2 + X3 + X4, X458 >= 0, X2 >= 0, X4 >= 0
   mark(z) -{ 2 }-> a__uTake2(1 + mark(X1194) + X2183, X2, X3, X4) :|: X1194 >= 0, X2183 >= 0, z = 1 + (1 + X1194 + X2183) + X2 + X3 + X4, X3 >= 0, X2 >= 0, X4 >= 0
   mark(z) -{ 3 }-> a__uTake2(1 + 0 + 3, X2, X3, X4) :|: X3 >= 0, z = 1 + 3 + X2 + X3 + X4, X2 >= 0, X4 >= 0
   mark(z) -{ 2 }-> a__uTake1(a__uTake2(mark(X1187), X2176, X3103, X450)) :|: X2176 >= 0, X1187 >= 0, X3103 >= 0, z = 1 + (1 + X1187 + X2176 + X3103 + X450), X450 >= 0
   mark(z) -{ 2 }-> a__uTake1(a__uTake1(mark(z - 2))) :|: z - 2 >= 0
   mark(z) -{ 2 }-> a__uTake1(a__uLength(mark(X1188), X2177)) :|: X1188 >= 0, X2177 >= 0, z = 1 + (1 + X1188 + X2177)
   mark(z) -{ 2 }-> a__uTake1(a__take(mark(X1186), mark(X2175))) :|: X1186 >= 0, z = 1 + (1 + X1186 + X2175), X2175 >= 0
   mark(z) -{ 2 }-> a__uTake1(a__length(mark(z - 2))) :|: z - 2 >= 0
   mark(z) -{ 2 }-> a__uTake1(a__isNatList(z - 2)) :|: z - 2 >= 0
   mark(z) -{ 2 }-> a__uTake1(a__isNatIList(z - 2)) :|: z - 2 >= 0
   mark(z) -{ 2 }-> a__uTake1(a__isNat(z - 2)) :|: z - 2 >= 0
   mark(z) -{ 2 }-> a__uTake1(a__and(mark(X1185), mark(X2174))) :|: X1185 >= 0, z = 1 + (1 + X1185 + X2174), X2174 >= 0
   mark(z) -{ 2 }-> a__uTake1(1 + mark(z - 2)) :|: z - 2 >= 0
   mark(z) -{ 2 }-> a__uTake1(1 + mark(X1189) + X2178) :|: X2178 >= 0, X1189 >= 0, z = 1 + (1 + X1189 + X2178)
   mark(z) -{ 2 }-> a__uLength(a__uTake2(mark(X1197), X2186, X3105, X464), X2) :|: X2186 >= 0, X3105 >= 0, X1197 >= 0, X2 >= 0, z = 1 + (1 + X1197 + X2186 + X3105 + X464) + X2, X464 >= 0
   mark(z) -{ 2 }-> a__uLength(a__uTake1(mark(X463)), X2) :|: X463 >= 0, z = 1 + (1 + X463) + X2, X2 >= 0
   mark(z) -{ 2 }-> a__uLength(a__uLength(mark(X1198), X2187), X2) :|: X1198 >= 0, X2187 >= 0, z = 1 + (1 + X1198 + X2187) + X2, X2 >= 0
   mark(z) -{ 2 }-> a__uLength(a__take(mark(X1196), mark(X2185)), X2) :|: X1196 >= 0, X2 >= 0, z = 1 + (1 + X1196 + X2185) + X2, X2185 >= 0
   mark(z) -{ 2 }-> a__uLength(a__length(mark(X462)), X2) :|: z = 1 + (1 + X462) + X2, X462 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__uLength(a__isNatList(X460), X2) :|: X460 >= 0, z = 1 + (1 + X460) + X2, X2 >= 0
   mark(z) -{ 2 }-> a__uLength(a__isNatIList(X459), X2) :|: z = 1 + (1 + X459) + X2, X459 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__uLength(a__isNat(X461), X2) :|: X461 >= 0, z = 1 + (1 + X461) + X2, X2 >= 0
   mark(z) -{ 2 }-> a__uLength(a__and(mark(X1195), mark(X2184)), X2) :|: X1195 >= 0, X2184 >= 0, X2 >= 0, z = 1 + (1 + X1195 + X2184) + X2
   mark(z) -{ 3 }-> a__uLength(3, z - 4) :|: z - 4 >= 0
   mark(z) -{ 2 }-> a__uLength(2, z - 3) :|: z - 3 >= 0
   mark(z) -{ 2 }-> a__uLength(1, z - 2) :|: z - 2 >= 0
   mark(z) -{ 2 }-> a__uLength(0, z - 1) :|: z - 1 >= 0
   mark(z) -{ 2 }-> a__uLength(1 + mark(X465), X2) :|: X2 >= 0, z = 1 + (1 + X465) + X2, X465 >= 0
   mark(z) -{ 2 }-> a__uLength(1 + mark(X1199) + X2188, X2) :|: z = 1 + (1 + X1199 + X2188) + X2, X2188 >= 0, X2 >= 0, X1199 >= 0
   mark(z) -{ 3 }-> a__uLength(1 + 0 + 3, z - 4) :|: z - 4 >= 0
   mark(z) -{ 1 }-> a__take(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   mark(z) -{ 2 }-> a__length(a__uTake2(mark(X1102), X286, X324, X423)) :|: X286 >= 0, X324 >= 0, X423 >= 0, z = 1 + (1 + X1102 + X286 + X324 + X423), X1102 >= 0
   mark(z) -{ 2 }-> a__length(a__uTake1(mark(z - 2))) :|: z - 2 >= 0
   mark(z) -{ 2 }-> a__length(a__uLength(mark(X1103), X287)) :|: z = 1 + (1 + X1103 + X287), X287 >= 0, X1103 >= 0
   mark(z) -{ 2 }-> a__length(a__take(mark(X1101), mark(X285))) :|: X1101 >= 0, z = 1 + (1 + X1101 + X285), X285 >= 0
   mark(z) -{ 2 }-> a__length(a__length(mark(z - 2))) :|: z - 2 >= 0
   mark(z) -{ 2 }-> a__length(a__isNatList(z - 2)) :|: z - 2 >= 0
   mark(z) -{ 2 }-> a__length(a__isNatIList(z - 2)) :|: z - 2 >= 0
   mark(z) -{ 2 }-> a__length(a__isNat(z - 2)) :|: z - 2 >= 0
   mark(z) -{ 2 }-> a__length(a__and(mark(X1100), mark(X284))) :|: X1100 >= 0, X284 >= 0, z = 1 + (1 + X1100 + X284)
   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(X1104) + X288) :|: z = 1 + (1 + X1104 + X288), X1104 >= 0, X288 >= 0
   mark(z) -{ 3 }-> a__length(1 + 0 + 3) :|: z = 1 + 3
   mark(z) -{ 1 }-> a__isNatList(z - 1) :|: z - 1 >= 0
   mark(z) -{ 1 }-> a__isNatIList(z - 1) :|: z - 1 >= 0
   mark(z) -{ 1 }-> a__isNat(z - 1) :|: z - 1 >= 0
   mark(z) -{ 1 }-> a__and(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   mark(z) -{ 2 }-> 3 :|: z = 3
   mark(z) -{ 1 }-> 2 :|: z = 2
   mark(z) -{ 1 }-> 1 :|: z = 1
   mark(z) -{ 3 }-> 1 :|: z = 1 + 2, 2 = 2
   mark(z) -{ 1 }-> 0 :|: z = 0
   mark(z) -{ 3 }-> 1 + X :|: z = 1 + 2, X >= 0, 2 = X
   mark(z) -{ 3 }-> 1 + X :|: z = 1 + 0, X >= 0, 0 = X
   mark(z) -{ 3 }-> 1 + X :|: z = 1 + 1, X >= 0, 1 = X
   mark(z) -{ 4 }-> 1 + X :|: z = 1 + 3, X >= 0, 3 = X
   mark(z) -{ 4 }-> 1 + X :|: z = 1 + 3, X >= 0, 1 + 0 + 3 = X
   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


----------------------------------------

(41) CpxTrsToCdtProof (UPPER BOUND(ID))
Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT
----------------------------------------

(42)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__AND(z0, z1) -> c1
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNATILIST(zeros) -> c3
   A__ISNATILIST(cons(z0, z1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNAT(z0))
   A__ISNATILIST(cons(z0, z1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNATILIST(z1))
   A__ISNATILIST(z0) -> c6
   A__ISNAT(0) -> c7
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__ISNAT(z0) -> c10
   A__ISNATLIST(nil) -> c11
   A__ISNATLIST(cons(z0, z1)) -> c12(A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
   A__ISNATLIST(cons(z0, z1)) -> c13(A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__ISNATLIST(take(z0, z1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNAT(z0))
   A__ISNATLIST(take(z0, z1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNATILIST(z1))
   A__ISNATLIST(z0) -> c16
   A__ZEROS -> c17
   A__ZEROS -> c18
   A__TAKE(0, z0) -> c19(A__UTAKE1(a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(z0), cons(z1, z2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__ISNAT(z0))
   A__TAKE(s(z0), cons(z1, z2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNAT(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNATILIST(z2))
   A__TAKE(z0, z1) -> c23
   A__UTAKE1(tt) -> c24
   A__UTAKE1(z0) -> c25
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   A__UTAKE2(z0, z1, z2, z3) -> c27
   A__LENGTH(cons(z0, z1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
   A__LENGTH(cons(z0, z1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__LENGTH(z0) -> c30
   A__ULENGTH(tt, z0) -> c31(A__LENGTH(mark(z0)), MARK(z0))
   A__ULENGTH(z0, z1) -> c32
   MARK(and(z0, z1)) -> c33(A__AND(mark(z0), mark(z1)), MARK(z0))
   MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
   MARK(zeros) -> c39(A__ZEROS)
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake1(z0)) -> c42(A__UTAKE1(mark(z0)), MARK(z0))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(tt) -> c45
   MARK(0) -> c46
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   MARK(nil) -> c49
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__AND(z0, z1) -> c1
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNATILIST(zeros) -> c3
   A__ISNATILIST(cons(z0, z1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNAT(z0))
   A__ISNATILIST(cons(z0, z1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNATILIST(z1))
   A__ISNATILIST(z0) -> c6
   A__ISNAT(0) -> c7
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__ISNAT(z0) -> c10
   A__ISNATLIST(nil) -> c11
   A__ISNATLIST(cons(z0, z1)) -> c12(A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
   A__ISNATLIST(cons(z0, z1)) -> c13(A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__ISNATLIST(take(z0, z1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNAT(z0))
   A__ISNATLIST(take(z0, z1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNATILIST(z1))
   A__ISNATLIST(z0) -> c16
   A__ZEROS -> c17
   A__ZEROS -> c18
   A__TAKE(0, z0) -> c19(A__UTAKE1(a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(z0), cons(z1, z2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__ISNAT(z0))
   A__TAKE(s(z0), cons(z1, z2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNAT(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNATILIST(z2))
   A__TAKE(z0, z1) -> c23
   A__UTAKE1(tt) -> c24
   A__UTAKE1(z0) -> c25
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   A__UTAKE2(z0, z1, z2, z3) -> c27
   A__LENGTH(cons(z0, z1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
   A__LENGTH(cons(z0, z1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__LENGTH(z0) -> c30
   A__ULENGTH(tt, z0) -> c31(A__LENGTH(mark(z0)), MARK(z0))
   A__ULENGTH(z0, z1) -> c32
   MARK(and(z0, z1)) -> c33(A__AND(mark(z0), mark(z1)), MARK(z0))
   MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
   MARK(zeros) -> c39(A__ZEROS)
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake1(z0)) -> c42(A__UTAKE1(mark(z0)), MARK(z0))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(tt) -> c45
   MARK(0) -> c46
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   MARK(nil) -> c49
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__ISNATLIST_1, A__ZEROS, A__TAKE_2, A__UTAKE1_1, A__UTAKE2_4, A__LENGTH_1, A__ULENGTH_2, MARK_1

Compound Symbols:   c_1, c1, c2_1, c3, c4_2, c5_2, c6, c7, c8_1, c9_1, c10, c11, c12_2, c13_2, c14_2, c15_2, c16, c17, c18, c19_2, c20_3, c21_4, c22_4, c23, c24, c25, c26_1, c27, c28_3, c29_3, c30, c31_2, c32, c33_2, c34_2, c35_1, c36_1, c37_1, c38_2, c39_1, c40_2, c41_2, c42_2, c43_2, c44_2, c45, c46, c47_1, c48_1, c49


----------------------------------------

(43) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 19 trailing nodes:
   A__UTAKE1(tt) -> c24
   A__ULENGTH(z0, z1) -> c32
   MARK(tt) -> c45
   A__LENGTH(z0) -> c30
   A__UTAKE2(z0, z1, z2, z3) -> c27
   A__UTAKE1(z0) -> c25
   A__AND(z0, z1) -> c1
   A__ZEROS -> c18
   A__ISNAT(z0) -> c10
   A__ISNAT(0) -> c7
   A__ISNATILIST(zeros) -> c3
   A__ZEROS -> c17
   A__ISNATLIST(nil) -> c11
   A__TAKE(z0, z1) -> c23
   MARK(zeros) -> c39(A__ZEROS)
   A__ISNATILIST(z0) -> c6
   MARK(nil) -> c49
   MARK(0) -> c46
   A__ISNATLIST(z0) -> c16

----------------------------------------

(44)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNATILIST(cons(z0, z1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNAT(z0))
   A__ISNATILIST(cons(z0, z1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNATILIST(z1))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__ISNATLIST(cons(z0, z1)) -> c12(A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
   A__ISNATLIST(cons(z0, z1)) -> c13(A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__ISNATLIST(take(z0, z1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNAT(z0))
   A__ISNATLIST(take(z0, z1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNATILIST(z1))
   A__TAKE(0, z0) -> c19(A__UTAKE1(a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(z0), cons(z1, z2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__ISNAT(z0))
   A__TAKE(s(z0), cons(z1, z2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNAT(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNATILIST(z2))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   A__LENGTH(cons(z0, z1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
   A__LENGTH(cons(z0, z1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__ULENGTH(tt, z0) -> c31(A__LENGTH(mark(z0)), MARK(z0))
   MARK(and(z0, z1)) -> c33(A__AND(mark(z0), mark(z1)), MARK(z0))
   MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake1(z0)) -> c42(A__UTAKE1(mark(z0)), MARK(z0))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNATILIST(cons(z0, z1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNAT(z0))
   A__ISNATILIST(cons(z0, z1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNATILIST(z1))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__ISNATLIST(cons(z0, z1)) -> c12(A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
   A__ISNATLIST(cons(z0, z1)) -> c13(A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__ISNATLIST(take(z0, z1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNAT(z0))
   A__ISNATLIST(take(z0, z1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNATILIST(z1))
   A__TAKE(0, z0) -> c19(A__UTAKE1(a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(z0), cons(z1, z2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__ISNAT(z0))
   A__TAKE(s(z0), cons(z1, z2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNAT(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNATILIST(z2))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   A__LENGTH(cons(z0, z1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
   A__LENGTH(cons(z0, z1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__ULENGTH(tt, z0) -> c31(A__LENGTH(mark(z0)), MARK(z0))
   MARK(and(z0, z1)) -> c33(A__AND(mark(z0), mark(z1)), MARK(z0))
   MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake1(z0)) -> c42(A__UTAKE1(mark(z0)), MARK(z0))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__ISNATLIST_1, A__TAKE_2, A__UTAKE2_4, A__LENGTH_1, A__ULENGTH_2, MARK_1

Compound Symbols:   c_1, c2_1, c4_2, c5_2, c8_1, c9_1, c12_2, c13_2, c14_2, c15_2, c19_2, c20_3, c21_4, c22_4, c26_1, c28_3, c29_3, c31_2, c33_2, c34_2, c35_1, c36_1, c37_1, c38_2, c40_2, c41_2, c42_2, c43_2, c44_2, c47_1, c48_1


----------------------------------------

(45) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing tuple parts
----------------------------------------

(46)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNATILIST(cons(z0, z1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNAT(z0))
   A__ISNATILIST(cons(z0, z1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNATILIST(z1))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__ISNATLIST(cons(z0, z1)) -> c12(A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
   A__ISNATLIST(cons(z0, z1)) -> c13(A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__ISNATLIST(take(z0, z1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNAT(z0))
   A__ISNATLIST(take(z0, z1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNATILIST(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__ISNAT(z0))
   A__TAKE(s(z0), cons(z1, z2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNAT(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNATILIST(z2))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   A__LENGTH(cons(z0, z1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
   A__LENGTH(cons(z0, z1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__ULENGTH(tt, z0) -> c31(A__LENGTH(mark(z0)), MARK(z0))
   MARK(and(z0, z1)) -> c33(A__AND(mark(z0), mark(z1)), MARK(z0))
   MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNATILIST(cons(z0, z1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNAT(z0))
   A__ISNATILIST(cons(z0, z1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNATILIST(z1))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__ISNATLIST(cons(z0, z1)) -> c12(A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
   A__ISNATLIST(cons(z0, z1)) -> c13(A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__ISNATLIST(take(z0, z1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNAT(z0))
   A__ISNATLIST(take(z0, z1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNATILIST(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__ISNAT(z0))
   A__TAKE(s(z0), cons(z1, z2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNAT(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNATILIST(z2))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   A__LENGTH(cons(z0, z1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
   A__LENGTH(cons(z0, z1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__ULENGTH(tt, z0) -> c31(A__LENGTH(mark(z0)), MARK(z0))
   MARK(and(z0, z1)) -> c33(A__AND(mark(z0), mark(z1)), MARK(z0))
   MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__ISNATLIST_1, A__TAKE_2, A__UTAKE2_4, A__LENGTH_1, A__ULENGTH_2, MARK_1

Compound Symbols:   c_1, c2_1, c4_2, c5_2, c8_1, c9_1, c12_2, c13_2, c14_2, c15_2, c20_3, c21_4, c22_4, c26_1, c28_3, c29_3, c31_2, c33_2, c34_2, c35_1, c36_1, c37_1, c38_2, c40_2, c41_2, c43_2, c44_2, c47_1, c48_1, c19_1, c42_1


----------------------------------------

(47) CdtToCpxRelTrsProof (BOTH BOUNDS(ID, ID))
Converted S to standard rules, and D \ S as well as R to relative rules.
----------------------------------------

(48)
Obligation:
The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF).


The TRS R consists of the following rules:

   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNATILIST(cons(z0, z1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNAT(z0))
   A__ISNATILIST(cons(z0, z1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNATILIST(z1))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__ISNATLIST(cons(z0, z1)) -> c12(A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
   A__ISNATLIST(cons(z0, z1)) -> c13(A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__ISNATLIST(take(z0, z1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNAT(z0))
   A__ISNATLIST(take(z0, z1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNATILIST(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__ISNAT(z0))
   A__TAKE(s(z0), cons(z1, z2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNAT(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNATILIST(z2))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   A__LENGTH(cons(z0, z1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
   A__LENGTH(cons(z0, z1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__ULENGTH(tt, z0) -> c31(A__LENGTH(mark(z0)), MARK(z0))
   MARK(and(z0, z1)) -> c33(A__AND(mark(z0), mark(z1)), MARK(z0))
   MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))

The (relative) TRS S consists of the following rules:

   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil

Rewrite Strategy: INNERMOST
----------------------------------------

(49) RelTrsToTrsProof (UPPER BOUND(ID))
transformed relative TRS to TRS
----------------------------------------

(50)
Obligation:
The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF).


The TRS R consists of the following rules:

   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNATILIST(cons(z0, z1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNAT(z0))
   A__ISNATILIST(cons(z0, z1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNATILIST(z1))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__ISNATLIST(cons(z0, z1)) -> c12(A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
   A__ISNATLIST(cons(z0, z1)) -> c13(A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__ISNATLIST(take(z0, z1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNAT(z0))
   A__ISNATLIST(take(z0, z1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNATILIST(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__ISNAT(z0))
   A__TAKE(s(z0), cons(z1, z2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNAT(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNATILIST(z2))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   A__LENGTH(cons(z0, z1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
   A__LENGTH(cons(z0, z1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__ULENGTH(tt, z0) -> c31(A__LENGTH(mark(z0)), MARK(z0))
   MARK(and(z0, z1)) -> c33(A__AND(mark(z0), mark(z1)), MARK(z0))
   MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil

S is empty.
Rewrite Strategy: INNERMOST
----------------------------------------

(51) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID))
Transformed relative TRS to weighted TRS
----------------------------------------

(52)
Obligation:
The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, INF).


The TRS R consists of the following rules:

   A__AND(tt, z0) -> c(MARK(z0)) [1]
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0)) [1]
   A__ISNATILIST(cons(z0, z1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNAT(z0)) [1]
   A__ISNATILIST(cons(z0, z1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNATILIST(z1)) [1]
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0)) [1]
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0)) [1]
   A__ISNATLIST(cons(z0, z1)) -> c12(A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0)) [1]
   A__ISNATLIST(cons(z0, z1)) -> c13(A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1)) [1]
   A__ISNATLIST(take(z0, z1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNAT(z0)) [1]
   A__ISNATLIST(take(z0, z1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNATILIST(z1)) [1]
   A__TAKE(s(z0), cons(z1, z2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__ISNAT(z0)) [1]
   A__TAKE(s(z0), cons(z1, z2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNAT(z1)) [1]
   A__TAKE(s(z0), cons(z1, z2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNATILIST(z2)) [1]
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1)) [1]
   A__LENGTH(cons(z0, z1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0)) [1]
   A__LENGTH(cons(z0, z1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1)) [1]
   A__ULENGTH(tt, z0) -> c31(A__LENGTH(mark(z0)), MARK(z0)) [1]
   MARK(and(z0, z1)) -> c33(A__AND(mark(z0), mark(z1)), MARK(z0)) [1]
   MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1)) [1]
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0)) [1]
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0)) [1]
   MARK(isNat(z0)) -> c37(A__ISNAT(z0)) [1]
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0)) [1]
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0)) [1]
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1)) [1]
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0)) [1]
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0)) [1]
   MARK(s(z0)) -> c47(MARK(z0)) [1]
   MARK(cons(z0, z1)) -> c48(MARK(z0)) [1]
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0)) [1]
   MARK(uTake1(z0)) -> c42(MARK(z0)) [1]
   a__and(tt, z0) -> mark(z0) [0]
   a__and(z0, z1) -> and(z0, z1) [0]
   a__isNatIList(z0) -> a__isNatList(z0) [0]
   a__isNatIList(zeros) -> tt [0]
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1)) [0]
   a__isNatIList(z0) -> isNatIList(z0) [0]
   a__isNat(0) -> tt [0]
   a__isNat(s(z0)) -> a__isNat(z0) [0]
   a__isNat(length(z0)) -> a__isNatList(z0) [0]
   a__isNat(z0) -> isNat(z0) [0]
   a__isNatList(nil) -> tt [0]
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1)) [0]
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1)) [0]
   a__isNatList(z0) -> isNatList(z0) [0]
   a__zeros -> cons(0, zeros) [0]
   a__zeros -> zeros [0]
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0)) [0]
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2) [0]
   a__take(z0, z1) -> take(z0, z1) [0]
   a__uTake1(tt) -> nil [0]
   a__uTake1(z0) -> uTake1(z0) [0]
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2)) [0]
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3) [0]
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1) [0]
   a__length(z0) -> length(z0) [0]
   a__uLength(tt, z0) -> s(a__length(mark(z0))) [0]
   a__uLength(z0, z1) -> uLength(z0, z1) [0]
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1)) [0]
   mark(isNatIList(z0)) -> a__isNatIList(z0) [0]
   mark(isNatList(z0)) -> a__isNatList(z0) [0]
   mark(isNat(z0)) -> a__isNat(z0) [0]
   mark(length(z0)) -> a__length(mark(z0)) [0]
   mark(zeros) -> a__zeros [0]
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) [0]
   mark(uTake1(z0)) -> a__uTake1(mark(z0)) [0]
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3) [0]
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1) [0]
   mark(tt) -> tt [0]
   mark(0) -> 0 [0]
   mark(s(z0)) -> s(mark(z0)) [0]
   mark(cons(z0, z1)) -> cons(mark(z0), z1) [0]
   mark(nil) -> nil [0]

Rewrite Strategy: INNERMOST
----------------------------------------

(53) TypeInferenceProof (BOTH BOUNDS(ID, ID))
Infered types.
----------------------------------------

(54)
Obligation:
Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   A__AND(tt, z0) -> c(MARK(z0)) [1]
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0)) [1]
   A__ISNATILIST(cons(z0, z1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNAT(z0)) [1]
   A__ISNATILIST(cons(z0, z1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNATILIST(z1)) [1]
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0)) [1]
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0)) [1]
   A__ISNATLIST(cons(z0, z1)) -> c12(A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0)) [1]
   A__ISNATLIST(cons(z0, z1)) -> c13(A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1)) [1]
   A__ISNATLIST(take(z0, z1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNAT(z0)) [1]
   A__ISNATLIST(take(z0, z1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNATILIST(z1)) [1]
   A__TAKE(s(z0), cons(z1, z2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__ISNAT(z0)) [1]
   A__TAKE(s(z0), cons(z1, z2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNAT(z1)) [1]
   A__TAKE(s(z0), cons(z1, z2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNATILIST(z2)) [1]
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1)) [1]
   A__LENGTH(cons(z0, z1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0)) [1]
   A__LENGTH(cons(z0, z1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1)) [1]
   A__ULENGTH(tt, z0) -> c31(A__LENGTH(mark(z0)), MARK(z0)) [1]
   MARK(and(z0, z1)) -> c33(A__AND(mark(z0), mark(z1)), MARK(z0)) [1]
   MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1)) [1]
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0)) [1]
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0)) [1]
   MARK(isNat(z0)) -> c37(A__ISNAT(z0)) [1]
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0)) [1]
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0)) [1]
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1)) [1]
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0)) [1]
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0)) [1]
   MARK(s(z0)) -> c47(MARK(z0)) [1]
   MARK(cons(z0, z1)) -> c48(MARK(z0)) [1]
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0)) [1]
   MARK(uTake1(z0)) -> c42(MARK(z0)) [1]
   a__and(tt, z0) -> mark(z0) [0]
   a__and(z0, z1) -> and(z0, z1) [0]
   a__isNatIList(z0) -> a__isNatList(z0) [0]
   a__isNatIList(zeros) -> tt [0]
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1)) [0]
   a__isNatIList(z0) -> isNatIList(z0) [0]
   a__isNat(0) -> tt [0]
   a__isNat(s(z0)) -> a__isNat(z0) [0]
   a__isNat(length(z0)) -> a__isNatList(z0) [0]
   a__isNat(z0) -> isNat(z0) [0]
   a__isNatList(nil) -> tt [0]
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1)) [0]
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1)) [0]
   a__isNatList(z0) -> isNatList(z0) [0]
   a__zeros -> cons(0, zeros) [0]
   a__zeros -> zeros [0]
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0)) [0]
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2) [0]
   a__take(z0, z1) -> take(z0, z1) [0]
   a__uTake1(tt) -> nil [0]
   a__uTake1(z0) -> uTake1(z0) [0]
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2)) [0]
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3) [0]
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1) [0]
   a__length(z0) -> length(z0) [0]
   a__uLength(tt, z0) -> s(a__length(mark(z0))) [0]
   a__uLength(z0, z1) -> uLength(z0, z1) [0]
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1)) [0]
   mark(isNatIList(z0)) -> a__isNatIList(z0) [0]
   mark(isNatList(z0)) -> a__isNatList(z0) [0]
   mark(isNat(z0)) -> a__isNat(z0) [0]
   mark(length(z0)) -> a__length(mark(z0)) [0]
   mark(zeros) -> a__zeros [0]
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) [0]
   mark(uTake1(z0)) -> a__uTake1(mark(z0)) [0]
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3) [0]
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1) [0]
   mark(tt) -> tt [0]
   mark(0) -> 0 [0]
   mark(s(z0)) -> s(mark(z0)) [0]
   mark(cons(z0, z1)) -> cons(mark(z0), z1) [0]
   mark(nil) -> nil [0]

The TRS has the following type information:
A__AND :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil -> c
tt :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil
c :: c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42 -> c
MARK :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil -> c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42
A__ISNATILIST :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil -> c2:c4:c5
c2 :: c12:c13:c14:c15 -> c2:c4:c5
A__ISNATLIST :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil -> c12:c13:c14:c15
cons :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil
c4 :: c -> c8:c9 -> c2:c4:c5
a__isNat :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil
a__isNatIList :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil
A__ISNAT :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil -> c8:c9
c5 :: c -> c2:c4:c5 -> c2:c4:c5
s :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil
c8 :: c8:c9 -> c8:c9
length :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil
c9 :: c12:c13:c14:c15 -> c8:c9
c12 :: c -> c8:c9 -> c12:c13:c14:c15
a__isNatList :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil
c13 :: c -> c12:c13:c14:c15 -> c12:c13:c14:c15
take :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil
c14 :: c -> c8:c9 -> c12:c13:c14:c15
c15 :: c -> c2:c4:c5 -> c12:c13:c14:c15
A__TAKE :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil -> c20:c21:c22:c19
c20 :: c26 -> c -> c8:c9 -> c20:c21:c22:c19
A__UTAKE2 :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil -> c26
a__and :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil
c21 :: c26 -> c -> c -> c8:c9 -> c20:c21:c22:c19
c22 :: c26 -> c -> c -> c2:c4:c5 -> c20:c21:c22:c19
c26 :: c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42 -> c26
A__LENGTH :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil -> c28:c29
c28 :: c31 -> c -> c8:c9 -> c28:c29
A__ULENGTH :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil -> c31
c29 :: c31 -> c -> c12:c13:c14:c15 -> c28:c29
c31 :: c28:c29 -> c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42 -> c31
mark :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil
and :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil
c33 :: c -> c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42 -> c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42
c34 :: c -> c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42 -> c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42
isNatIList :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil
c35 :: c2:c4:c5 -> c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42
isNatList :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil
c36 :: c12:c13:c14:c15 -> c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42
isNat :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil
c37 :: c8:c9 -> c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42
c38 :: c28:c29 -> c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42 -> c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42
c40 :: c20:c21:c22:c19 -> c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42 -> c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42
c41 :: c20:c21:c22:c19 -> c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42 -> c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42
uTake2 :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil
c43 :: c26 -> c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42 -> c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42
uLength :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil
c44 :: c31 -> c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42 -> c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42
c47 :: c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42 -> c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42
c48 :: c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42 -> c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42
0 :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil
c19 :: c2:c4:c5 -> c20:c21:c22:c19
uTake1 :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil
c42 :: c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42 -> c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42
zeros :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil
nil :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil
a__zeros :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil
a__take :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil
a__uTake1 :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil
a__uTake2 :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil
a__length :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil
a__uLength :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil

Rewrite Strategy: INNERMOST
----------------------------------------

(55) CompletionProof (UPPER BOUND(ID))
The transformation into a RNTS is sound, since:

(a) The obligation is a constructor system where every type has a constant constructor,

(b) The following defined symbols do not have to be completely defined, as they can never occur inside other defined symbols:

   A__AND_2
   A__ISNATILIST_1
   A__ISNAT_1
   A__ISNATLIST_1
   A__TAKE_2
   A__UTAKE2_4
   A__LENGTH_1
   A__ULENGTH_2
   MARK_1

(c) The following functions are completely defined:

   a__and_2
   a__isNatIList_1
   a__isNat_1
   a__isNatList_1
   a__zeros
   a__take_2
   a__uTake1_1
   a__uTake2_4
   a__length_1
   a__uLength_2
   mark_1

Due to the following rules being added:

   a__and(v0, v1) -> null_a__and [0]
   a__isNatIList(v0) -> null_a__isNatIList [0]
   a__isNat(v0) -> null_a__isNat [0]
   a__isNatList(v0) -> null_a__isNatList [0]
   a__zeros -> null_a__zeros [0]
   a__take(v0, v1) -> null_a__take [0]
   a__uTake1(v0) -> null_a__uTake1 [0]
   a__uTake2(v0, v1, v2, v3) -> null_a__uTake2 [0]
   a__length(v0) -> null_a__length [0]
   a__uLength(v0, v1) -> null_a__uLength [0]
   mark(v0) -> null_mark [0]

And the following fresh constants:    null_a__and, null_a__isNatIList, null_a__isNat, null_a__isNatList, null_a__zeros, null_a__take, null_a__uTake1, null_a__uTake2, null_a__length, null_a__uLength, null_mark, const, const1, const2, const3, const4, const5, const6, const7, const8

----------------------------------------

(56)
Obligation:
Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is:

Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   A__AND(tt, z0) -> c(MARK(z0)) [1]
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0)) [1]
   A__ISNATILIST(cons(z0, z1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNAT(z0)) [1]
   A__ISNATILIST(cons(z0, z1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNATILIST(z1)) [1]
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0)) [1]
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0)) [1]
   A__ISNATLIST(cons(z0, z1)) -> c12(A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0)) [1]
   A__ISNATLIST(cons(z0, z1)) -> c13(A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1)) [1]
   A__ISNATLIST(take(z0, z1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNAT(z0)) [1]
   A__ISNATLIST(take(z0, z1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNATILIST(z1)) [1]
   A__TAKE(s(z0), cons(z1, z2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__ISNAT(z0)) [1]
   A__TAKE(s(z0), cons(z1, z2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNAT(z1)) [1]
   A__TAKE(s(z0), cons(z1, z2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNATILIST(z2)) [1]
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1)) [1]
   A__LENGTH(cons(z0, z1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0)) [1]
   A__LENGTH(cons(z0, z1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1)) [1]
   A__ULENGTH(tt, z0) -> c31(A__LENGTH(mark(z0)), MARK(z0)) [1]
   MARK(and(z0, z1)) -> c33(A__AND(mark(z0), mark(z1)), MARK(z0)) [1]
   MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1)) [1]
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0)) [1]
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0)) [1]
   MARK(isNat(z0)) -> c37(A__ISNAT(z0)) [1]
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0)) [1]
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0)) [1]
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1)) [1]
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0)) [1]
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0)) [1]
   MARK(s(z0)) -> c47(MARK(z0)) [1]
   MARK(cons(z0, z1)) -> c48(MARK(z0)) [1]
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0)) [1]
   MARK(uTake1(z0)) -> c42(MARK(z0)) [1]
   a__and(tt, z0) -> mark(z0) [0]
   a__and(z0, z1) -> and(z0, z1) [0]
   a__isNatIList(z0) -> a__isNatList(z0) [0]
   a__isNatIList(zeros) -> tt [0]
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1)) [0]
   a__isNatIList(z0) -> isNatIList(z0) [0]
   a__isNat(0) -> tt [0]
   a__isNat(s(z0)) -> a__isNat(z0) [0]
   a__isNat(length(z0)) -> a__isNatList(z0) [0]
   a__isNat(z0) -> isNat(z0) [0]
   a__isNatList(nil) -> tt [0]
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1)) [0]
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1)) [0]
   a__isNatList(z0) -> isNatList(z0) [0]
   a__zeros -> cons(0, zeros) [0]
   a__zeros -> zeros [0]
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0)) [0]
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2) [0]
   a__take(z0, z1) -> take(z0, z1) [0]
   a__uTake1(tt) -> nil [0]
   a__uTake1(z0) -> uTake1(z0) [0]
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2)) [0]
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3) [0]
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1) [0]
   a__length(z0) -> length(z0) [0]
   a__uLength(tt, z0) -> s(a__length(mark(z0))) [0]
   a__uLength(z0, z1) -> uLength(z0, z1) [0]
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1)) [0]
   mark(isNatIList(z0)) -> a__isNatIList(z0) [0]
   mark(isNatList(z0)) -> a__isNatList(z0) [0]
   mark(isNat(z0)) -> a__isNat(z0) [0]
   mark(length(z0)) -> a__length(mark(z0)) [0]
   mark(zeros) -> a__zeros [0]
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) [0]
   mark(uTake1(z0)) -> a__uTake1(mark(z0)) [0]
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3) [0]
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1) [0]
   mark(tt) -> tt [0]
   mark(0) -> 0 [0]
   mark(s(z0)) -> s(mark(z0)) [0]
   mark(cons(z0, z1)) -> cons(mark(z0), z1) [0]
   mark(nil) -> nil [0]
   a__and(v0, v1) -> null_a__and [0]
   a__isNatIList(v0) -> null_a__isNatIList [0]
   a__isNat(v0) -> null_a__isNat [0]
   a__isNatList(v0) -> null_a__isNatList [0]
   a__zeros -> null_a__zeros [0]
   a__take(v0, v1) -> null_a__take [0]
   a__uTake1(v0) -> null_a__uTake1 [0]
   a__uTake2(v0, v1, v2, v3) -> null_a__uTake2 [0]
   a__length(v0) -> null_a__length [0]
   a__uLength(v0, v1) -> null_a__uLength [0]
   mark(v0) -> null_mark [0]

The TRS has the following type information:
A__AND :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> c
tt :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark
c :: c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42 -> c
MARK :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42
A__ISNATILIST :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> c2:c4:c5
c2 :: c12:c13:c14:c15 -> c2:c4:c5
A__ISNATLIST :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> c12:c13:c14:c15
cons :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark
c4 :: c -> c8:c9 -> c2:c4:c5
a__isNat :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark
a__isNatIList :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark
A__ISNAT :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> c8:c9
c5 :: c -> c2:c4:c5 -> c2:c4:c5
s :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark
c8 :: c8:c9 -> c8:c9
length :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark
c9 :: c12:c13:c14:c15 -> c8:c9
c12 :: c -> c8:c9 -> c12:c13:c14:c15
a__isNatList :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark
c13 :: c -> c12:c13:c14:c15 -> c12:c13:c14:c15
take :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark
c14 :: c -> c8:c9 -> c12:c13:c14:c15
c15 :: c -> c2:c4:c5 -> c12:c13:c14:c15
A__TAKE :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> c20:c21:c22:c19
c20 :: c26 -> c -> c8:c9 -> c20:c21:c22:c19
A__UTAKE2 :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> c26
a__and :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark
c21 :: c26 -> c -> c -> c8:c9 -> c20:c21:c22:c19
c22 :: c26 -> c -> c -> c2:c4:c5 -> c20:c21:c22:c19
c26 :: c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42 -> c26
A__LENGTH :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> c28:c29
c28 :: c31 -> c -> c8:c9 -> c28:c29
A__ULENGTH :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> c31
c29 :: c31 -> c -> c12:c13:c14:c15 -> c28:c29
c31 :: c28:c29 -> c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42 -> c31
mark :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark
and :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark
c33 :: c -> c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42 -> c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42
c34 :: c -> c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42 -> c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42
isNatIList :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark
c35 :: c2:c4:c5 -> c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42
isNatList :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark
c36 :: c12:c13:c14:c15 -> c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42
isNat :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark
c37 :: c8:c9 -> c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42
c38 :: c28:c29 -> c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42 -> c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42
c40 :: c20:c21:c22:c19 -> c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42 -> c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42
c41 :: c20:c21:c22:c19 -> c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42 -> c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42
uTake2 :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark
c43 :: c26 -> c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42 -> c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42
uLength :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark
c44 :: c31 -> c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42 -> c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42
c47 :: c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42 -> c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42
c48 :: c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42 -> c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42
0 :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark
c19 :: c2:c4:c5 -> c20:c21:c22:c19
uTake1 :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark
c42 :: c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42 -> c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42
zeros :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark
nil :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark
a__zeros :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark
a__take :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark
a__uTake1 :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark
a__uTake2 :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark
a__length :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark
a__uLength :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark
null_a__and :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark
null_a__isNatIList :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark
null_a__isNat :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark
null_a__isNatList :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark
null_a__zeros :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark
null_a__take :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark
null_a__uTake1 :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark
null_a__uTake2 :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark
null_a__length :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark
null_a__uLength :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark
null_mark :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark
const :: c
const1 :: c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42
const2 :: c2:c4:c5
const3 :: c12:c13:c14:c15
const4 :: c8:c9
const5 :: c20:c21:c22:c19
const6 :: c26
const7 :: c28:c29
const8 :: c31

Rewrite Strategy: INNERMOST
----------------------------------------

(57) CompletionProof (UPPER BOUND(ID))
The TRS is a completely defined constructor system, as every type has a constant constructor and the following rules were added:

   a__and(v0, v1) -> null_a__and [0]
   a__isNatIList(v0) -> null_a__isNatIList [0]
   a__isNat(v0) -> null_a__isNat [0]
   a__isNatList(v0) -> null_a__isNatList [0]
   a__zeros -> null_a__zeros [0]
   a__take(v0, v1) -> null_a__take [0]
   a__uTake1(v0) -> null_a__uTake1 [0]
   a__uTake2(v0, v1, v2, v3) -> null_a__uTake2 [0]
   a__length(v0) -> null_a__length [0]
   a__uLength(v0, v1) -> null_a__uLength [0]
   mark(v0) -> null_mark [0]
   A__AND(v0, v1) -> null_A__AND [0]
   A__ISNAT(v0) -> null_A__ISNAT [0]
   A__ISNATLIST(v0) -> null_A__ISNATLIST [0]
   A__TAKE(v0, v1) -> null_A__TAKE [0]
   A__UTAKE2(v0, v1, v2, v3) -> null_A__UTAKE2 [0]
   A__LENGTH(v0) -> null_A__LENGTH [0]
   A__ULENGTH(v0, v1) -> null_A__ULENGTH [0]
   MARK(v0) -> null_MARK [0]

And the following fresh constants:    null_a__and, null_a__isNatIList, null_a__isNat, null_a__isNatList, null_a__zeros, null_a__take, null_a__uTake1, null_a__uTake2, null_a__length, null_a__uLength, null_mark, null_A__AND, null_A__ISNAT, null_A__ISNATLIST, null_A__TAKE, null_A__UTAKE2, null_A__LENGTH, null_A__ULENGTH, null_MARK, const

----------------------------------------

(58)
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__AND(tt, z0) -> c(MARK(z0)) [1]
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0)) [1]
   A__ISNATILIST(cons(z0, z1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNAT(z0)) [1]
   A__ISNATILIST(cons(z0, z1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNATILIST(z1)) [1]
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0)) [1]
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0)) [1]
   A__ISNATLIST(cons(z0, z1)) -> c12(A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0)) [1]
   A__ISNATLIST(cons(z0, z1)) -> c13(A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1)) [1]
   A__ISNATLIST(take(z0, z1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNAT(z0)) [1]
   A__ISNATLIST(take(z0, z1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNATILIST(z1)) [1]
   A__TAKE(s(z0), cons(z1, z2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__ISNAT(z0)) [1]
   A__TAKE(s(z0), cons(z1, z2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNAT(z1)) [1]
   A__TAKE(s(z0), cons(z1, z2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNATILIST(z2)) [1]
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1)) [1]
   A__LENGTH(cons(z0, z1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0)) [1]
   A__LENGTH(cons(z0, z1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1)) [1]
   A__ULENGTH(tt, z0) -> c31(A__LENGTH(mark(z0)), MARK(z0)) [1]
   MARK(and(z0, z1)) -> c33(A__AND(mark(z0), mark(z1)), MARK(z0)) [1]
   MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1)) [1]
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0)) [1]
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0)) [1]
   MARK(isNat(z0)) -> c37(A__ISNAT(z0)) [1]
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0)) [1]
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0)) [1]
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1)) [1]
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0)) [1]
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0)) [1]
   MARK(s(z0)) -> c47(MARK(z0)) [1]
   MARK(cons(z0, z1)) -> c48(MARK(z0)) [1]
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0)) [1]
   MARK(uTake1(z0)) -> c42(MARK(z0)) [1]
   a__and(tt, z0) -> mark(z0) [0]
   a__and(z0, z1) -> and(z0, z1) [0]
   a__isNatIList(z0) -> a__isNatList(z0) [0]
   a__isNatIList(zeros) -> tt [0]
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1)) [0]
   a__isNatIList(z0) -> isNatIList(z0) [0]
   a__isNat(0) -> tt [0]
   a__isNat(s(z0)) -> a__isNat(z0) [0]
   a__isNat(length(z0)) -> a__isNatList(z0) [0]
   a__isNat(z0) -> isNat(z0) [0]
   a__isNatList(nil) -> tt [0]
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1)) [0]
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1)) [0]
   a__isNatList(z0) -> isNatList(z0) [0]
   a__zeros -> cons(0, zeros) [0]
   a__zeros -> zeros [0]
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0)) [0]
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2) [0]
   a__take(z0, z1) -> take(z0, z1) [0]
   a__uTake1(tt) -> nil [0]
   a__uTake1(z0) -> uTake1(z0) [0]
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2)) [0]
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3) [0]
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1) [0]
   a__length(z0) -> length(z0) [0]
   a__uLength(tt, z0) -> s(a__length(mark(z0))) [0]
   a__uLength(z0, z1) -> uLength(z0, z1) [0]
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1)) [0]
   mark(isNatIList(z0)) -> a__isNatIList(z0) [0]
   mark(isNatList(z0)) -> a__isNatList(z0) [0]
   mark(isNat(z0)) -> a__isNat(z0) [0]
   mark(length(z0)) -> a__length(mark(z0)) [0]
   mark(zeros) -> a__zeros [0]
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) [0]
   mark(uTake1(z0)) -> a__uTake1(mark(z0)) [0]
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3) [0]
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1) [0]
   mark(tt) -> tt [0]
   mark(0) -> 0 [0]
   mark(s(z0)) -> s(mark(z0)) [0]
   mark(cons(z0, z1)) -> cons(mark(z0), z1) [0]
   mark(nil) -> nil [0]
   a__and(v0, v1) -> null_a__and [0]
   a__isNatIList(v0) -> null_a__isNatIList [0]
   a__isNat(v0) -> null_a__isNat [0]
   a__isNatList(v0) -> null_a__isNatList [0]
   a__zeros -> null_a__zeros [0]
   a__take(v0, v1) -> null_a__take [0]
   a__uTake1(v0) -> null_a__uTake1 [0]
   a__uTake2(v0, v1, v2, v3) -> null_a__uTake2 [0]
   a__length(v0) -> null_a__length [0]
   a__uLength(v0, v1) -> null_a__uLength [0]
   mark(v0) -> null_mark [0]
   A__AND(v0, v1) -> null_A__AND [0]
   A__ISNAT(v0) -> null_A__ISNAT [0]
   A__ISNATLIST(v0) -> null_A__ISNATLIST [0]
   A__TAKE(v0, v1) -> null_A__TAKE [0]
   A__UTAKE2(v0, v1, v2, v3) -> null_A__UTAKE2 [0]
   A__LENGTH(v0) -> null_A__LENGTH [0]
   A__ULENGTH(v0, v1) -> null_A__ULENGTH [0]
   MARK(v0) -> null_MARK [0]

The TRS has the following type information:
A__AND :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> c:null_A__AND
tt :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark
c :: c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42:null_MARK -> c:null_A__AND
MARK :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42:null_MARK
A__ISNATILIST :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> c2:c4:c5
c2 :: c12:c13:c14:c15:null_A__ISNATLIST -> c2:c4:c5
A__ISNATLIST :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> c12:c13:c14:c15:null_A__ISNATLIST
cons :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark
c4 :: c:null_A__AND -> c8:c9:null_A__ISNAT -> c2:c4:c5
a__isNat :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark
a__isNatIList :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark
A__ISNAT :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> c8:c9:null_A__ISNAT
c5 :: c:null_A__AND -> c2:c4:c5 -> c2:c4:c5
s :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark
c8 :: c8:c9:null_A__ISNAT -> c8:c9:null_A__ISNAT
length :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark
c9 :: c12:c13:c14:c15:null_A__ISNATLIST -> c8:c9:null_A__ISNAT
c12 :: c:null_A__AND -> c8:c9:null_A__ISNAT -> c12:c13:c14:c15:null_A__ISNATLIST
a__isNatList :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark
c13 :: c:null_A__AND -> c12:c13:c14:c15:null_A__ISNATLIST -> c12:c13:c14:c15:null_A__ISNATLIST
take :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark
c14 :: c:null_A__AND -> c8:c9:null_A__ISNAT -> c12:c13:c14:c15:null_A__ISNATLIST
c15 :: c:null_A__AND -> c2:c4:c5 -> c12:c13:c14:c15:null_A__ISNATLIST
A__TAKE :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> c20:c21:c22:c19:null_A__TAKE
c20 :: c26:null_A__UTAKE2 -> c:null_A__AND -> c8:c9:null_A__ISNAT -> c20:c21:c22:c19:null_A__TAKE
A__UTAKE2 :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> c26:null_A__UTAKE2
a__and :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark
c21 :: c26:null_A__UTAKE2 -> c:null_A__AND -> c:null_A__AND -> c8:c9:null_A__ISNAT -> c20:c21:c22:c19:null_A__TAKE
c22 :: c26:null_A__UTAKE2 -> c:null_A__AND -> c:null_A__AND -> c2:c4:c5 -> c20:c21:c22:c19:null_A__TAKE
c26 :: c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42:null_MARK -> c26:null_A__UTAKE2
A__LENGTH :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> c28:c29:null_A__LENGTH
c28 :: c31:null_A__ULENGTH -> c:null_A__AND -> c8:c9:null_A__ISNAT -> c28:c29:null_A__LENGTH
A__ULENGTH :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> c31:null_A__ULENGTH
c29 :: c31:null_A__ULENGTH -> c:null_A__AND -> c12:c13:c14:c15:null_A__ISNATLIST -> c28:c29:null_A__LENGTH
c31 :: c28:c29:null_A__LENGTH -> c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42:null_MARK -> c31:null_A__ULENGTH
mark :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark
and :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark
c33 :: c:null_A__AND -> c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42:null_MARK -> c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42:null_MARK
c34 :: c:null_A__AND -> c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42:null_MARK -> c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42:null_MARK
isNatIList :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark
c35 :: c2:c4:c5 -> c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42:null_MARK
isNatList :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark
c36 :: c12:c13:c14:c15:null_A__ISNATLIST -> c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42:null_MARK
isNat :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark
c37 :: c8:c9:null_A__ISNAT -> c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42:null_MARK
c38 :: c28:c29:null_A__LENGTH -> c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42:null_MARK -> c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42:null_MARK
c40 :: c20:c21:c22:c19:null_A__TAKE -> c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42:null_MARK -> c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42:null_MARK
c41 :: c20:c21:c22:c19:null_A__TAKE -> c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42:null_MARK -> c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42:null_MARK
uTake2 :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark
c43 :: c26:null_A__UTAKE2 -> c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42:null_MARK -> c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42:null_MARK
uLength :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark
c44 :: c31:null_A__ULENGTH -> c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42:null_MARK -> c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42:null_MARK
c47 :: c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42:null_MARK -> c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42:null_MARK
c48 :: c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42:null_MARK -> c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42:null_MARK
0 :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark
c19 :: c2:c4:c5 -> c20:c21:c22:c19:null_A__TAKE
uTake1 :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark
c42 :: c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42:null_MARK -> c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42:null_MARK
zeros :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark
nil :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark
a__zeros :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark
a__take :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark
a__uTake1 :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark
a__uTake2 :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark
a__length :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark
a__uLength :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark -> tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark
null_a__and :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark
null_a__isNatIList :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark
null_a__isNat :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark
null_a__isNatList :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark
null_a__zeros :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark
null_a__take :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark
null_a__uTake1 :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark
null_a__uTake2 :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark
null_a__length :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark
null_a__uLength :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark
null_mark :: tt:cons:s:length:take:and:isNatIList:isNatList:isNat:uTake2:uLength:0:uTake1:zeros:nil:null_a__and:null_a__isNatIList:null_a__isNat:null_a__isNatList:null_a__zeros:null_a__take:null_a__uTake1:null_a__uTake2:null_a__length:null_a__uLength:null_mark
null_A__AND :: c:null_A__AND
null_A__ISNAT :: c8:c9:null_A__ISNAT
null_A__ISNATLIST :: c12:c13:c14:c15:null_A__ISNATLIST
null_A__TAKE :: c20:c21:c22:c19:null_A__TAKE
null_A__UTAKE2 :: c26:null_A__UTAKE2
null_A__LENGTH :: c28:c29:null_A__LENGTH
null_A__ULENGTH :: c31:null_A__ULENGTH
null_MARK :: c33:c34:c35:c36:c37:c38:c40:c41:c43:c44:c47:c48:c42:null_MARK
const :: c2:c4:c5

Rewrite Strategy: INNERMOST
----------------------------------------

(59) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID))
Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction.
The constant constructors are abstracted as follows:

   tt => 2
   0 => 0
   zeros => 3
   nil => 1
   null_a__and => 0
   null_a__isNatIList => 0
   null_a__isNat => 0
   null_a__isNatList => 0
   null_a__zeros => 0
   null_a__take => 0
   null_a__uTake1 => 0
   null_a__uTake2 => 0
   null_a__length => 0
   null_a__uLength => 0
   null_mark => 0
   null_A__AND => 0
   null_A__ISNAT => 0
   null_A__ISNATLIST => 0
   null_A__TAKE => 0
   null_A__UTAKE2 => 0
   null_A__LENGTH => 0
   null_A__ULENGTH => 0
   null_MARK => 0
   const => 0

----------------------------------------

(60)
Obligation:
Complexity RNTS consisting of the following rules:

   A__AND(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   A__AND(z, z') -{ 1 }-> 1 + MARK(z0) :|: z = 2, z0 >= 0, z' = z0
   A__ISNAT(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   A__ISNAT(z) -{ 1 }-> 1 + A__ISNATLIST(z0) :|: z = 1 + z0, z0 >= 0
   A__ISNAT(z) -{ 1 }-> 1 + A__ISNAT(z0) :|: z = 1 + z0, z0 >= 0
   A__ISNATILIST(z) -{ 1 }-> 1 + A__ISNATLIST(z0) :|: z = z0, z0 >= 0
   A__ISNATILIST(z) -{ 1 }-> 1 + A__AND(a__isNat(z0), a__isNatIList(z1)) + A__ISNATILIST(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   A__ISNATILIST(z) -{ 1 }-> 1 + A__AND(a__isNat(z0), a__isNatIList(z1)) + A__ISNAT(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   A__ISNATLIST(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   A__ISNATLIST(z) -{ 1 }-> 1 + A__AND(a__isNat(z0), a__isNatList(z1)) + A__ISNATLIST(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   A__ISNATLIST(z) -{ 1 }-> 1 + A__AND(a__isNat(z0), a__isNatList(z1)) + A__ISNAT(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   A__ISNATLIST(z) -{ 1 }-> 1 + A__AND(a__isNat(z0), a__isNatIList(z1)) + A__ISNATILIST(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   A__ISNATLIST(z) -{ 1 }-> 1 + A__AND(a__isNat(z0), a__isNatIList(z1)) + A__ISNAT(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   A__LENGTH(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   A__LENGTH(z) -{ 1 }-> 1 + A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1) + A__AND(a__isNat(z0), a__isNatList(z1)) + A__ISNATLIST(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   A__LENGTH(z) -{ 1 }-> 1 + A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1) + A__AND(a__isNat(z0), a__isNatList(z1)) + A__ISNAT(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   A__TAKE(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   A__TAKE(z, z') -{ 1 }-> 1 + A__ISNATILIST(z0) :|: z0 >= 0, z = 0, z' = z0
   A__TAKE(z, z') -{ 1 }-> 1 + A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2) + A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))) + A__ISNAT(z0) :|: z1 >= 0, z' = 1 + z1 + z2, z = 1 + z0, z0 >= 0, z2 >= 0
   A__TAKE(z, z') -{ 1 }-> 1 + A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2) + A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))) + A__AND(a__isNat(z1), a__isNatIList(z2)) + A__ISNATILIST(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z = 1 + z0, z0 >= 0, z2 >= 0
   A__TAKE(z, z') -{ 1 }-> 1 + A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2) + A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))) + A__AND(a__isNat(z1), a__isNatIList(z2)) + A__ISNAT(z1) :|: z1 >= 0, z' = 1 + z1 + z2, z = 1 + z0, z0 >= 0, z2 >= 0
   A__ULENGTH(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   A__ULENGTH(z, z') -{ 1 }-> 1 + A__LENGTH(mark(z0)) + MARK(z0) :|: z = 2, z0 >= 0, z' = z0
   A__UTAKE2(z, z', z'', z4) -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, z4 = v3, v2 >= 0, v3 >= 0
   A__UTAKE2(z, z', z'', z4) -{ 1 }-> 1 + MARK(z1) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z2 >= 0, z'' = z1, z4 = z2
   MARK(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   MARK(z) -{ 1 }-> 1 + MARK(z0) :|: z = 1 + z0, z0 >= 0
   MARK(z) -{ 1 }-> 1 + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MARK(z) -{ 1 }-> 1 + A__ISNATLIST(z0) :|: z = 1 + z0, z0 >= 0
   MARK(z) -{ 1 }-> 1 + A__ISNATILIST(z0) :|: z = 1 + z0, z0 >= 0
   MARK(z) -{ 1 }-> 1 + A__ISNAT(z0) :|: z = 1 + z0, z0 >= 0
   MARK(z) -{ 1 }-> 1 + A__UTAKE2(mark(z0), z1, z2, z3) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 + z2 + z3, z2 >= 0, z3 >= 0
   MARK(z) -{ 1 }-> 1 + A__ULENGTH(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MARK(z) -{ 1 }-> 1 + A__TAKE(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MARK(z) -{ 1 }-> 1 + A__TAKE(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MARK(z) -{ 1 }-> 1 + A__LENGTH(mark(z0)) + MARK(z0) :|: z = 1 + z0, z0 >= 0
   MARK(z) -{ 1 }-> 1 + A__AND(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MARK(z) -{ 1 }-> 1 + A__AND(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   a__and(z, z') -{ 0 }-> mark(z0) :|: z = 2, z0 >= 0, z' = z0
   a__and(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   a__and(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0
   a__isNat(z) -{ 0 }-> a__isNatList(z0) :|: z = 1 + z0, z0 >= 0
   a__isNat(z) -{ 0 }-> a__isNat(z0) :|: z = 1 + z0, z0 >= 0
   a__isNat(z) -{ 0 }-> 2 :|: z = 0
   a__isNat(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   a__isNat(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   a__isNatIList(z) -{ 0 }-> a__isNatList(z0) :|: z = z0, z0 >= 0
   a__isNatIList(z) -{ 0 }-> a__and(a__isNat(z0), a__isNatIList(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   a__isNatIList(z) -{ 0 }-> 2 :|: z = 3
   a__isNatIList(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   a__isNatIList(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   a__isNatList(z) -{ 0 }-> a__and(a__isNat(z0), a__isNatList(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   a__isNatList(z) -{ 0 }-> a__and(a__isNat(z0), a__isNatIList(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   a__isNatList(z) -{ 0 }-> 2 :|: z = 1
   a__isNatList(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   a__isNatList(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   a__length(z) -{ 0 }-> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   a__length(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   a__length(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   a__take(z, z') -{ 0 }-> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2) :|: z1 >= 0, z' = 1 + z1 + z2, z = 1 + z0, z0 >= 0, z2 >= 0
   a__take(z, z') -{ 0 }-> a__uTake1(a__isNatIList(z0)) :|: z0 >= 0, z = 0, z' = z0
   a__take(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   a__take(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0
   a__uLength(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   a__uLength(z, z') -{ 0 }-> 1 + a__length(mark(z0)) :|: z = 2, z0 >= 0, z' = z0
   a__uLength(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0
   a__uTake1(z) -{ 0 }-> 1 :|: z = 2
   a__uTake1(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   a__uTake1(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   a__uTake2(z, z', z'', z4) -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, z4 = v3, v2 >= 0, v3 >= 0
   a__uTake2(z, z', z'', z4) -{ 0 }-> 1 + mark(z1) + (1 + z0 + z2) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z2 >= 0, z'' = z1, z4 = z2
   a__uTake2(z, z', z'', z4) -{ 0 }-> 1 + z0 + z1 + z2 + z3 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z4 = z3, z2 >= 0, z3 >= 0
   a__zeros -{ 0 }-> 3 :|: 
   a__zeros -{ 0 }-> 0 :|: 
   a__zeros -{ 0 }-> 1 + 0 + 3 :|: 
   mark(z) -{ 0 }-> a__zeros :|: z = 3
   mark(z) -{ 0 }-> a__uTake2(mark(z0), z1, z2, z3) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 + z2 + z3, z2 >= 0, z3 >= 0
   mark(z) -{ 0 }-> a__uTake1(mark(z0)) :|: z = 1 + z0, z0 >= 0
   mark(z) -{ 0 }-> a__uLength(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   mark(z) -{ 0 }-> a__take(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   mark(z) -{ 0 }-> a__length(mark(z0)) :|: z = 1 + z0, z0 >= 0
   mark(z) -{ 0 }-> a__isNatList(z0) :|: z = 1 + z0, z0 >= 0
   mark(z) -{ 0 }-> a__isNatIList(z0) :|: z = 1 + z0, z0 >= 0
   mark(z) -{ 0 }-> a__isNat(z0) :|: z = 1 + z0, z0 >= 0
   mark(z) -{ 0 }-> a__and(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   mark(z) -{ 0 }-> 2 :|: z = 2
   mark(z) -{ 0 }-> 1 :|: z = 1
   mark(z) -{ 0 }-> 0 :|: z = 0
   mark(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   mark(z) -{ 0 }-> 1 + mark(z0) :|: z = 1 + z0, z0 >= 0
   mark(z) -{ 0 }-> 1 + mark(z0) + z1 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1

Only complete derivations are relevant for the runtime complexity.

----------------------------------------

(61) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__ISNATILIST(cons(z0, z1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNAT(z0)) by 
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__AND(isNat(z0), a__isNatIList(x1)), A__ISNAT(z0))

----------------------------------------

(62)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNATILIST(cons(z0, z1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNATILIST(z1))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__ISNATLIST(cons(z0, z1)) -> c12(A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
   A__ISNATLIST(cons(z0, z1)) -> c13(A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__ISNATLIST(take(z0, z1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNAT(z0))
   A__ISNATLIST(take(z0, z1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNATILIST(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__ISNAT(z0))
   A__TAKE(s(z0), cons(z1, z2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNAT(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNATILIST(z2))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   A__LENGTH(cons(z0, z1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
   A__LENGTH(cons(z0, z1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__ULENGTH(tt, z0) -> c31(A__LENGTH(mark(z0)), MARK(z0))
   MARK(and(z0, z1)) -> c33(A__AND(mark(z0), mark(z1)), MARK(z0))
   MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__AND(isNat(z0), a__isNatIList(x1)), A__ISNAT(z0))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNATILIST(cons(z0, z1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNATILIST(z1))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__ISNATLIST(cons(z0, z1)) -> c12(A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
   A__ISNATLIST(cons(z0, z1)) -> c13(A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__ISNATLIST(take(z0, z1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNAT(z0))
   A__ISNATLIST(take(z0, z1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNATILIST(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__ISNAT(z0))
   A__TAKE(s(z0), cons(z1, z2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNAT(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNATILIST(z2))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   A__LENGTH(cons(z0, z1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
   A__LENGTH(cons(z0, z1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__ULENGTH(tt, z0) -> c31(A__LENGTH(mark(z0)), MARK(z0))
   MARK(and(z0, z1)) -> c33(A__AND(mark(z0), mark(z1)), MARK(z0))
   MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__AND(isNat(z0), a__isNatIList(x1)), A__ISNAT(z0))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__ISNATLIST_1, A__TAKE_2, A__UTAKE2_4, A__LENGTH_1, A__ULENGTH_2, MARK_1

Compound Symbols:   c_1, c2_1, c5_2, c8_1, c9_1, c12_2, c13_2, c14_2, c15_2, c20_3, c21_4, c22_4, c26_1, c28_3, c29_3, c31_2, c33_2, c34_2, c35_1, c36_1, c37_1, c38_2, c40_2, c41_2, c43_2, c44_2, c47_1, c48_1, c19_1, c42_1, c4_2


----------------------------------------

(63) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing tuple parts
----------------------------------------

(64)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNATILIST(cons(z0, z1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNATILIST(z1))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__ISNATLIST(cons(z0, z1)) -> c12(A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
   A__ISNATLIST(cons(z0, z1)) -> c13(A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__ISNATLIST(take(z0, z1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNAT(z0))
   A__ISNATLIST(take(z0, z1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNATILIST(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__ISNAT(z0))
   A__TAKE(s(z0), cons(z1, z2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNAT(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNATILIST(z2))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   A__LENGTH(cons(z0, z1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
   A__LENGTH(cons(z0, z1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__ULENGTH(tt, z0) -> c31(A__LENGTH(mark(z0)), MARK(z0))
   MARK(and(z0, z1)) -> c33(A__AND(mark(z0), mark(z1)), MARK(z0))
   MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNATILIST(cons(z0, z1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNATILIST(z1))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__ISNATLIST(cons(z0, z1)) -> c12(A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
   A__ISNATLIST(cons(z0, z1)) -> c13(A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__ISNATLIST(take(z0, z1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNAT(z0))
   A__ISNATLIST(take(z0, z1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNATILIST(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__ISNAT(z0))
   A__TAKE(s(z0), cons(z1, z2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNAT(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNATILIST(z2))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   A__LENGTH(cons(z0, z1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
   A__LENGTH(cons(z0, z1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__ULENGTH(tt, z0) -> c31(A__LENGTH(mark(z0)), MARK(z0))
   MARK(and(z0, z1)) -> c33(A__AND(mark(z0), mark(z1)), MARK(z0))
   MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__ISNATLIST_1, A__TAKE_2, A__UTAKE2_4, A__LENGTH_1, A__ULENGTH_2, MARK_1

Compound Symbols:   c_1, c2_1, c5_2, c8_1, c9_1, c12_2, c13_2, c14_2, c15_2, c20_3, c21_4, c22_4, c26_1, c28_3, c29_3, c31_2, c33_2, c34_2, c35_1, c36_1, c37_1, c38_2, c40_2, c41_2, c43_2, c44_2, c47_1, c48_1, c19_1, c42_1, c4_2, c4_1


----------------------------------------

(65) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__ISNATILIST(cons(z0, z1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNATILIST(z1)) by 
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__AND(isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))

----------------------------------------

(66)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__ISNATLIST(cons(z0, z1)) -> c12(A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
   A__ISNATLIST(cons(z0, z1)) -> c13(A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__ISNATLIST(take(z0, z1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNAT(z0))
   A__ISNATLIST(take(z0, z1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNATILIST(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__ISNAT(z0))
   A__TAKE(s(z0), cons(z1, z2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNAT(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNATILIST(z2))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   A__LENGTH(cons(z0, z1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
   A__LENGTH(cons(z0, z1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__ULENGTH(tt, z0) -> c31(A__LENGTH(mark(z0)), MARK(z0))
   MARK(and(z0, z1)) -> c33(A__AND(mark(z0), mark(z1)), MARK(z0))
   MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__AND(isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__ISNATLIST(cons(z0, z1)) -> c12(A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
   A__ISNATLIST(cons(z0, z1)) -> c13(A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__ISNATLIST(take(z0, z1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNAT(z0))
   A__ISNATLIST(take(z0, z1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNATILIST(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__ISNAT(z0))
   A__TAKE(s(z0), cons(z1, z2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNAT(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNATILIST(z2))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   A__LENGTH(cons(z0, z1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
   A__LENGTH(cons(z0, z1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__ULENGTH(tt, z0) -> c31(A__LENGTH(mark(z0)), MARK(z0))
   MARK(and(z0, z1)) -> c33(A__AND(mark(z0), mark(z1)), MARK(z0))
   MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__AND(isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__ISNATLIST_1, A__TAKE_2, A__UTAKE2_4, A__LENGTH_1, A__ULENGTH_2, MARK_1

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c12_2, c13_2, c14_2, c15_2, c20_3, c21_4, c22_4, c26_1, c28_3, c29_3, c31_2, c33_2, c34_2, c35_1, c36_1, c37_1, c38_2, c40_2, c41_2, c43_2, c44_2, c47_1, c48_1, c19_1, c42_1, c4_2, c4_1, c5_2


----------------------------------------

(67) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing tuple parts
----------------------------------------

(68)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__ISNATLIST(cons(z0, z1)) -> c12(A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
   A__ISNATLIST(cons(z0, z1)) -> c13(A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__ISNATLIST(take(z0, z1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNAT(z0))
   A__ISNATLIST(take(z0, z1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNATILIST(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__ISNAT(z0))
   A__TAKE(s(z0), cons(z1, z2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNAT(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNATILIST(z2))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   A__LENGTH(cons(z0, z1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
   A__LENGTH(cons(z0, z1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__ULENGTH(tt, z0) -> c31(A__LENGTH(mark(z0)), MARK(z0))
   MARK(and(z0, z1)) -> c33(A__AND(mark(z0), mark(z1)), MARK(z0))
   MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__ISNATLIST(cons(z0, z1)) -> c12(A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
   A__ISNATLIST(cons(z0, z1)) -> c13(A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__ISNATLIST(take(z0, z1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNAT(z0))
   A__ISNATLIST(take(z0, z1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNATILIST(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__ISNAT(z0))
   A__TAKE(s(z0), cons(z1, z2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNAT(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNATILIST(z2))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   A__LENGTH(cons(z0, z1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
   A__LENGTH(cons(z0, z1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__ULENGTH(tt, z0) -> c31(A__LENGTH(mark(z0)), MARK(z0))
   MARK(and(z0, z1)) -> c33(A__AND(mark(z0), mark(z1)), MARK(z0))
   MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__ISNATLIST_1, A__TAKE_2, A__UTAKE2_4, A__LENGTH_1, A__ULENGTH_2, MARK_1

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c12_2, c13_2, c14_2, c15_2, c20_3, c21_4, c22_4, c26_1, c28_3, c29_3, c31_2, c33_2, c34_2, c35_1, c36_1, c37_1, c38_2, c40_2, c41_2, c43_2, c44_2, c47_1, c48_1, c19_1, c42_1, c4_2, c4_1, c5_2, c5_1


----------------------------------------

(69) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__ISNATLIST(cons(z0, z1)) -> c12(A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0)) by 
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)), A__ISNAT(0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__AND(isNat(z0), a__isNatList(x1)), A__ISNAT(z0))

----------------------------------------

(70)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__ISNATLIST(cons(z0, z1)) -> c13(A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__ISNATLIST(take(z0, z1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNAT(z0))
   A__ISNATLIST(take(z0, z1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNATILIST(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__ISNAT(z0))
   A__TAKE(s(z0), cons(z1, z2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNAT(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNATILIST(z2))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   A__LENGTH(cons(z0, z1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
   A__LENGTH(cons(z0, z1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__ULENGTH(tt, z0) -> c31(A__LENGTH(mark(z0)), MARK(z0))
   MARK(and(z0, z1)) -> c33(A__AND(mark(z0), mark(z1)), MARK(z0))
   MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)), A__ISNAT(0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__AND(isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__ISNATLIST(cons(z0, z1)) -> c13(A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__ISNATLIST(take(z0, z1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNAT(z0))
   A__ISNATLIST(take(z0, z1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNATILIST(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__ISNAT(z0))
   A__TAKE(s(z0), cons(z1, z2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNAT(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNATILIST(z2))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   A__LENGTH(cons(z0, z1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
   A__LENGTH(cons(z0, z1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__ULENGTH(tt, z0) -> c31(A__LENGTH(mark(z0)), MARK(z0))
   MARK(and(z0, z1)) -> c33(A__AND(mark(z0), mark(z1)), MARK(z0))
   MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)), A__ISNAT(0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__AND(isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__ISNATLIST_1, A__TAKE_2, A__UTAKE2_4, A__LENGTH_1, A__ULENGTH_2, MARK_1

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c13_2, c14_2, c15_2, c20_3, c21_4, c22_4, c26_1, c28_3, c29_3, c31_2, c33_2, c34_2, c35_1, c36_1, c37_1, c38_2, c40_2, c41_2, c43_2, c44_2, c47_1, c48_1, c19_1, c42_1, c4_2, c4_1, c5_2, c5_1, c12_2


----------------------------------------

(71) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing tuple parts
----------------------------------------

(72)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__ISNATLIST(cons(z0, z1)) -> c13(A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__ISNATLIST(take(z0, z1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNAT(z0))
   A__ISNATLIST(take(z0, z1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNATILIST(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__ISNAT(z0))
   A__TAKE(s(z0), cons(z1, z2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNAT(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNATILIST(z2))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   A__LENGTH(cons(z0, z1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
   A__LENGTH(cons(z0, z1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__ULENGTH(tt, z0) -> c31(A__LENGTH(mark(z0)), MARK(z0))
   MARK(and(z0, z1)) -> c33(A__AND(mark(z0), mark(z1)), MARK(z0))
   MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__ISNATLIST(cons(z0, z1)) -> c13(A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__ISNATLIST(take(z0, z1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNAT(z0))
   A__ISNATLIST(take(z0, z1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNATILIST(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__ISNAT(z0))
   A__TAKE(s(z0), cons(z1, z2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNAT(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNATILIST(z2))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   A__LENGTH(cons(z0, z1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
   A__LENGTH(cons(z0, z1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__ULENGTH(tt, z0) -> c31(A__LENGTH(mark(z0)), MARK(z0))
   MARK(and(z0, z1)) -> c33(A__AND(mark(z0), mark(z1)), MARK(z0))
   MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__ISNATLIST_1, A__TAKE_2, A__UTAKE2_4, A__LENGTH_1, A__ULENGTH_2, MARK_1

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c13_2, c14_2, c15_2, c20_3, c21_4, c22_4, c26_1, c28_3, c29_3, c31_2, c33_2, c34_2, c35_1, c36_1, c37_1, c38_2, c40_2, c41_2, c43_2, c44_2, c47_1, c48_1, c19_1, c42_1, c4_2, c4_1, c5_2, c5_1, c12_2, c12_1


----------------------------------------

(73) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__ISNATLIST(cons(z0, z1)) -> c13(A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1)) by 
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt), A__ISNATLIST(nil))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__AND(isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))

----------------------------------------

(74)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__ISNATLIST(take(z0, z1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNAT(z0))
   A__ISNATLIST(take(z0, z1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNATILIST(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__ISNAT(z0))
   A__TAKE(s(z0), cons(z1, z2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNAT(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNATILIST(z2))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   A__LENGTH(cons(z0, z1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
   A__LENGTH(cons(z0, z1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__ULENGTH(tt, z0) -> c31(A__LENGTH(mark(z0)), MARK(z0))
   MARK(and(z0, z1)) -> c33(A__AND(mark(z0), mark(z1)), MARK(z0))
   MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt), A__ISNATLIST(nil))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__AND(isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__ISNATLIST(take(z0, z1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNAT(z0))
   A__ISNATLIST(take(z0, z1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNATILIST(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__ISNAT(z0))
   A__TAKE(s(z0), cons(z1, z2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNAT(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNATILIST(z2))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   A__LENGTH(cons(z0, z1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
   A__LENGTH(cons(z0, z1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__ULENGTH(tt, z0) -> c31(A__LENGTH(mark(z0)), MARK(z0))
   MARK(and(z0, z1)) -> c33(A__AND(mark(z0), mark(z1)), MARK(z0))
   MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt), A__ISNATLIST(nil))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__AND(isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__ISNATLIST_1, A__TAKE_2, A__UTAKE2_4, A__LENGTH_1, A__ULENGTH_2, MARK_1

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c14_2, c15_2, c20_3, c21_4, c22_4, c26_1, c28_3, c29_3, c31_2, c33_2, c34_2, c35_1, c36_1, c37_1, c38_2, c40_2, c41_2, c43_2, c44_2, c47_1, c48_1, c19_1, c42_1, c4_2, c4_1, c5_2, c5_1, c12_2, c12_1, c13_2


----------------------------------------

(75) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing tuple parts
----------------------------------------

(76)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__ISNATLIST(take(z0, z1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNAT(z0))
   A__ISNATLIST(take(z0, z1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNATILIST(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__ISNAT(z0))
   A__TAKE(s(z0), cons(z1, z2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNAT(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNATILIST(z2))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   A__LENGTH(cons(z0, z1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
   A__LENGTH(cons(z0, z1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__ULENGTH(tt, z0) -> c31(A__LENGTH(mark(z0)), MARK(z0))
   MARK(and(z0, z1)) -> c33(A__AND(mark(z0), mark(z1)), MARK(z0))
   MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__ISNATLIST(take(z0, z1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNAT(z0))
   A__ISNATLIST(take(z0, z1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNATILIST(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__ISNAT(z0))
   A__TAKE(s(z0), cons(z1, z2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNAT(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNATILIST(z2))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   A__LENGTH(cons(z0, z1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
   A__LENGTH(cons(z0, z1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__ULENGTH(tt, z0) -> c31(A__LENGTH(mark(z0)), MARK(z0))
   MARK(and(z0, z1)) -> c33(A__AND(mark(z0), mark(z1)), MARK(z0))
   MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__ISNATLIST_1, A__TAKE_2, A__UTAKE2_4, A__LENGTH_1, A__ULENGTH_2, MARK_1

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c14_2, c15_2, c20_3, c21_4, c22_4, c26_1, c28_3, c29_3, c31_2, c33_2, c34_2, c35_1, c36_1, c37_1, c38_2, c40_2, c41_2, c43_2, c44_2, c47_1, c48_1, c19_1, c42_1, c4_2, c4_1, c5_2, c5_1, c12_2, c12_1, c13_2, c13_1


----------------------------------------

(77) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__ISNATLIST(take(z0, z1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNAT(z0)) by 
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)), A__ISNAT(0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__AND(isNat(z0), a__isNatIList(x1)), A__ISNAT(z0))

----------------------------------------

(78)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__ISNATLIST(take(z0, z1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNATILIST(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__ISNAT(z0))
   A__TAKE(s(z0), cons(z1, z2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNAT(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNATILIST(z2))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   A__LENGTH(cons(z0, z1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
   A__LENGTH(cons(z0, z1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__ULENGTH(tt, z0) -> c31(A__LENGTH(mark(z0)), MARK(z0))
   MARK(and(z0, z1)) -> c33(A__AND(mark(z0), mark(z1)), MARK(z0))
   MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)), A__ISNAT(0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__AND(isNat(z0), a__isNatIList(x1)), A__ISNAT(z0))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__ISNATLIST(take(z0, z1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNATILIST(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__ISNAT(z0))
   A__TAKE(s(z0), cons(z1, z2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNAT(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNATILIST(z2))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   A__LENGTH(cons(z0, z1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
   A__LENGTH(cons(z0, z1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__ULENGTH(tt, z0) -> c31(A__LENGTH(mark(z0)), MARK(z0))
   MARK(and(z0, z1)) -> c33(A__AND(mark(z0), mark(z1)), MARK(z0))
   MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)), A__ISNAT(0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__AND(isNat(z0), a__isNatIList(x1)), A__ISNAT(z0))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__ISNATLIST_1, A__TAKE_2, A__UTAKE2_4, A__LENGTH_1, A__ULENGTH_2, MARK_1

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c15_2, c20_3, c21_4, c22_4, c26_1, c28_3, c29_3, c31_2, c33_2, c34_2, c35_1, c36_1, c37_1, c38_2, c40_2, c41_2, c43_2, c44_2, c47_1, c48_1, c19_1, c42_1, c4_2, c4_1, c5_2, c5_1, c12_2, c12_1, c13_2, c13_1, c14_2


----------------------------------------

(79) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing tuple parts
----------------------------------------

(80)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__ISNATLIST(take(z0, z1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNATILIST(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__ISNAT(z0))
   A__TAKE(s(z0), cons(z1, z2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNAT(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNATILIST(z2))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   A__LENGTH(cons(z0, z1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
   A__LENGTH(cons(z0, z1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__ULENGTH(tt, z0) -> c31(A__LENGTH(mark(z0)), MARK(z0))
   MARK(and(z0, z1)) -> c33(A__AND(mark(z0), mark(z1)), MARK(z0))
   MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__ISNATLIST(take(z0, z1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNATILIST(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__ISNAT(z0))
   A__TAKE(s(z0), cons(z1, z2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNAT(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNATILIST(z2))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   A__LENGTH(cons(z0, z1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
   A__LENGTH(cons(z0, z1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__ULENGTH(tt, z0) -> c31(A__LENGTH(mark(z0)), MARK(z0))
   MARK(and(z0, z1)) -> c33(A__AND(mark(z0), mark(z1)), MARK(z0))
   MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__ISNATLIST_1, A__TAKE_2, A__UTAKE2_4, A__LENGTH_1, A__ULENGTH_2, MARK_1

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c15_2, c20_3, c21_4, c22_4, c26_1, c28_3, c29_3, c31_2, c33_2, c34_2, c35_1, c36_1, c37_1, c38_2, c40_2, c41_2, c43_2, c44_2, c47_1, c48_1, c19_1, c42_1, c4_2, c4_1, c5_2, c5_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1


----------------------------------------

(81) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__ISNATLIST(take(z0, z1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(z1)), A__ISNATILIST(z1)) by 
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__AND(isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))

----------------------------------------

(82)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__TAKE(s(z0), cons(z1, z2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__ISNAT(z0))
   A__TAKE(s(z0), cons(z1, z2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNAT(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNATILIST(z2))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   A__LENGTH(cons(z0, z1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
   A__LENGTH(cons(z0, z1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__ULENGTH(tt, z0) -> c31(A__LENGTH(mark(z0)), MARK(z0))
   MARK(and(z0, z1)) -> c33(A__AND(mark(z0), mark(z1)), MARK(z0))
   MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__AND(isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__TAKE(s(z0), cons(z1, z2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__ISNAT(z0))
   A__TAKE(s(z0), cons(z1, z2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNAT(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNATILIST(z2))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   A__LENGTH(cons(z0, z1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
   A__LENGTH(cons(z0, z1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__ULENGTH(tt, z0) -> c31(A__LENGTH(mark(z0)), MARK(z0))
   MARK(and(z0, z1)) -> c33(A__AND(mark(z0), mark(z1)), MARK(z0))
   MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__AND(isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__TAKE_2, A__UTAKE2_4, A__LENGTH_1, A__ULENGTH_2, MARK_1, A__ISNATLIST_1

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c20_3, c21_4, c22_4, c26_1, c28_3, c29_3, c31_2, c33_2, c34_2, c35_1, c36_1, c37_1, c38_2, c40_2, c41_2, c43_2, c44_2, c47_1, c48_1, c19_1, c42_1, c4_2, c4_1, c5_2, c5_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2


----------------------------------------

(83) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing tuple parts
----------------------------------------

(84)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__TAKE(s(z0), cons(z1, z2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__ISNAT(z0))
   A__TAKE(s(z0), cons(z1, z2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNAT(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNATILIST(z2))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   A__LENGTH(cons(z0, z1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
   A__LENGTH(cons(z0, z1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__ULENGTH(tt, z0) -> c31(A__LENGTH(mark(z0)), MARK(z0))
   MARK(and(z0, z1)) -> c33(A__AND(mark(z0), mark(z1)), MARK(z0))
   MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__TAKE(s(z0), cons(z1, z2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__ISNAT(z0))
   A__TAKE(s(z0), cons(z1, z2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNAT(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNATILIST(z2))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   A__LENGTH(cons(z0, z1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
   A__LENGTH(cons(z0, z1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__ULENGTH(tt, z0) -> c31(A__LENGTH(mark(z0)), MARK(z0))
   MARK(and(z0, z1)) -> c33(A__AND(mark(z0), mark(z1)), MARK(z0))
   MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__TAKE_2, A__UTAKE2_4, A__LENGTH_1, A__ULENGTH_2, MARK_1, A__ISNATLIST_1

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c20_3, c21_4, c22_4, c26_1, c28_3, c29_3, c31_2, c33_2, c34_2, c35_1, c36_1, c37_1, c38_2, c40_2, c41_2, c43_2, c44_2, c47_1, c48_1, c19_1, c42_1, c4_2, c4_1, c5_2, c5_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c15_1


----------------------------------------

(85) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__TAKE(s(z0), cons(z1, z2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__ISNAT(z0)) by 
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(and(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))

----------------------------------------

(86)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__TAKE(s(z0), cons(z1, z2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNAT(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNATILIST(z2))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   A__LENGTH(cons(z0, z1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
   A__LENGTH(cons(z0, z1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__ULENGTH(tt, z0) -> c31(A__LENGTH(mark(z0)), MARK(z0))
   MARK(and(z0, z1)) -> c33(A__AND(mark(z0), mark(z1)), MARK(z0))
   MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(and(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__TAKE(s(z0), cons(z1, z2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNAT(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNATILIST(z2))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   A__LENGTH(cons(z0, z1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
   A__LENGTH(cons(z0, z1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__ULENGTH(tt, z0) -> c31(A__LENGTH(mark(z0)), MARK(z0))
   MARK(and(z0, z1)) -> c33(A__AND(mark(z0), mark(z1)), MARK(z0))
   MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(and(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__TAKE_2, A__UTAKE2_4, A__LENGTH_1, A__ULENGTH_2, MARK_1, A__ISNATLIST_1

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c21_4, c22_4, c26_1, c28_3, c29_3, c31_2, c33_2, c34_2, c35_1, c36_1, c37_1, c38_2, c40_2, c41_2, c43_2, c44_2, c47_1, c48_1, c19_1, c42_1, c4_2, c4_1, c5_2, c5_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c15_1, c20_3


----------------------------------------

(87) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing tuple parts
----------------------------------------

(88)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__TAKE(s(z0), cons(z1, z2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNAT(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNATILIST(z2))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   A__LENGTH(cons(z0, z1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
   A__LENGTH(cons(z0, z1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__ULENGTH(tt, z0) -> c31(A__LENGTH(mark(z0)), MARK(z0))
   MARK(and(z0, z1)) -> c33(A__AND(mark(z0), mark(z1)), MARK(z0))
   MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__TAKE(s(z0), cons(z1, z2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNAT(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNATILIST(z2))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   A__LENGTH(cons(z0, z1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
   A__LENGTH(cons(z0, z1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__ULENGTH(tt, z0) -> c31(A__LENGTH(mark(z0)), MARK(z0))
   MARK(and(z0, z1)) -> c33(A__AND(mark(z0), mark(z1)), MARK(z0))
   MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__TAKE_2, A__UTAKE2_4, A__LENGTH_1, A__ULENGTH_2, MARK_1, A__ISNATLIST_1

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c21_4, c22_4, c26_1, c28_3, c29_3, c31_2, c33_2, c34_2, c35_1, c36_1, c37_1, c38_2, c40_2, c41_2, c43_2, c44_2, c47_1, c48_1, c19_1, c42_1, c4_2, c4_1, c5_2, c5_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c15_1, c20_3, c20_2


----------------------------------------

(89) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__TAKE(s(z0), cons(z1, z2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNAT(z1)) by 
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(and(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNAT(0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))

----------------------------------------

(90)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__TAKE(s(z0), cons(z1, z2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNATILIST(z2))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   A__LENGTH(cons(z0, z1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
   A__LENGTH(cons(z0, z1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__ULENGTH(tt, z0) -> c31(A__LENGTH(mark(z0)), MARK(z0))
   MARK(and(z0, z1)) -> c33(A__AND(mark(z0), mark(z1)), MARK(z0))
   MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(and(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNAT(0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__TAKE(s(z0), cons(z1, z2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNATILIST(z2))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   A__LENGTH(cons(z0, z1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
   A__LENGTH(cons(z0, z1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__ULENGTH(tt, z0) -> c31(A__LENGTH(mark(z0)), MARK(z0))
   MARK(and(z0, z1)) -> c33(A__AND(mark(z0), mark(z1)), MARK(z0))
   MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(and(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNAT(0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__TAKE_2, A__UTAKE2_4, A__LENGTH_1, A__ULENGTH_2, MARK_1, A__ISNATLIST_1

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c22_4, c26_1, c28_3, c29_3, c31_2, c33_2, c34_2, c35_1, c36_1, c37_1, c38_2, c40_2, c41_2, c43_2, c44_2, c47_1, c48_1, c19_1, c42_1, c4_2, c4_1, c5_2, c5_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c15_1, c20_3, c20_2, c21_4


----------------------------------------

(91) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing tuple parts
----------------------------------------

(92)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__TAKE(s(z0), cons(z1, z2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNATILIST(z2))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   A__LENGTH(cons(z0, z1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
   A__LENGTH(cons(z0, z1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__ULENGTH(tt, z0) -> c31(A__LENGTH(mark(z0)), MARK(z0))
   MARK(and(z0, z1)) -> c33(A__AND(mark(z0), mark(z1)), MARK(z0))
   MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__TAKE(s(z0), cons(z1, z2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNATILIST(z2))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   A__LENGTH(cons(z0, z1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
   A__LENGTH(cons(z0, z1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__ULENGTH(tt, z0) -> c31(A__LENGTH(mark(z0)), MARK(z0))
   MARK(and(z0, z1)) -> c33(A__AND(mark(z0), mark(z1)), MARK(z0))
   MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__TAKE_2, A__UTAKE2_4, A__LENGTH_1, A__ULENGTH_2, MARK_1, A__ISNATLIST_1

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c22_4, c26_1, c28_3, c29_3, c31_2, c33_2, c34_2, c35_1, c36_1, c37_1, c38_2, c40_2, c41_2, c43_2, c44_2, c47_1, c48_1, c19_1, c42_1, c4_2, c4_1, c5_2, c5_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c15_1, c20_3, c20_2, c21_4, c21_3


----------------------------------------

(93) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__TAKE(s(z0), cons(z1, z2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2), A__AND(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), A__AND(a__isNat(z1), a__isNatIList(z2)), A__ISNATILIST(z2)) by 
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(and(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))

----------------------------------------

(94)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   A__LENGTH(cons(z0, z1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
   A__LENGTH(cons(z0, z1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__ULENGTH(tt, z0) -> c31(A__LENGTH(mark(z0)), MARK(z0))
   MARK(and(z0, z1)) -> c33(A__AND(mark(z0), mark(z1)), MARK(z0))
   MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(and(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   A__LENGTH(cons(z0, z1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
   A__LENGTH(cons(z0, z1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__ULENGTH(tt, z0) -> c31(A__LENGTH(mark(z0)), MARK(z0))
   MARK(and(z0, z1)) -> c33(A__AND(mark(z0), mark(z1)), MARK(z0))
   MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(and(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__UTAKE2_4, A__LENGTH_1, A__ULENGTH_2, MARK_1, A__TAKE_2, A__ISNATLIST_1

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c26_1, c28_3, c29_3, c31_2, c33_2, c34_2, c35_1, c36_1, c37_1, c38_2, c40_2, c41_2, c43_2, c44_2, c47_1, c48_1, c19_1, c42_1, c4_2, c4_1, c5_2, c5_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c15_1, c20_3, c20_2, c21_4, c21_3, c22_4


----------------------------------------

(95) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing tuple parts
----------------------------------------

(96)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   A__LENGTH(cons(z0, z1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
   A__LENGTH(cons(z0, z1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__ULENGTH(tt, z0) -> c31(A__LENGTH(mark(z0)), MARK(z0))
   MARK(and(z0, z1)) -> c33(A__AND(mark(z0), mark(z1)), MARK(z0))
   MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   A__LENGTH(cons(z0, z1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0))
   A__LENGTH(cons(z0, z1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__ULENGTH(tt, z0) -> c31(A__LENGTH(mark(z0)), MARK(z0))
   MARK(and(z0, z1)) -> c33(A__AND(mark(z0), mark(z1)), MARK(z0))
   MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__UTAKE2_4, A__LENGTH_1, A__ULENGTH_2, MARK_1, A__TAKE_2, A__ISNATLIST_1

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c26_1, c28_3, c29_3, c31_2, c33_2, c34_2, c35_1, c36_1, c37_1, c38_2, c40_2, c41_2, c43_2, c44_2, c47_1, c48_1, c19_1, c42_1, c4_2, c4_1, c5_2, c5_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c15_1, c20_3, c20_2, c21_4, c21_3, c22_4, c22_3


----------------------------------------

(97) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__LENGTH(cons(z0, z1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNAT(z0)) by 
   A__LENGTH(cons(x0, x1)) -> c28(A__ULENGTH(and(a__isNat(x0), a__isNatList(x1)), x1), A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c28(A__ULENGTH(a__and(a__isNat(x0), tt), nil), A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNAT(0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))

----------------------------------------

(98)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   A__LENGTH(cons(z0, z1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__ULENGTH(tt, z0) -> c31(A__LENGTH(mark(z0)), MARK(z0))
   MARK(and(z0, z1)) -> c33(A__AND(mark(z0), mark(z1)), MARK(z0))
   MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, x1)) -> c28(A__ULENGTH(and(a__isNat(x0), a__isNatList(x1)), x1), A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c28(A__ULENGTH(a__and(a__isNat(x0), tt), nil), A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNAT(0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   A__LENGTH(cons(z0, z1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__ULENGTH(tt, z0) -> c31(A__LENGTH(mark(z0)), MARK(z0))
   MARK(and(z0, z1)) -> c33(A__AND(mark(z0), mark(z1)), MARK(z0))
   MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, x1)) -> c28(A__ULENGTH(and(a__isNat(x0), a__isNatList(x1)), x1), A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c28(A__ULENGTH(a__and(a__isNat(x0), tt), nil), A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNAT(0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__UTAKE2_4, A__LENGTH_1, A__ULENGTH_2, MARK_1, A__TAKE_2, A__ISNATLIST_1

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c26_1, c29_3, c31_2, c33_2, c34_2, c35_1, c36_1, c37_1, c38_2, c40_2, c41_2, c43_2, c44_2, c47_1, c48_1, c19_1, c42_1, c4_2, c4_1, c5_2, c5_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c15_1, c20_3, c20_2, c21_4, c21_3, c22_4, c22_3, c28_3


----------------------------------------

(99) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing tuple parts
----------------------------------------

(100)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   A__LENGTH(cons(z0, z1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__ULENGTH(tt, z0) -> c31(A__LENGTH(mark(z0)), MARK(z0))
   MARK(and(z0, z1)) -> c33(A__AND(mark(z0), mark(z1)), MARK(z0))
   MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, nil)) -> c28(A__ULENGTH(a__and(a__isNat(x0), tt), nil), A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   A__LENGTH(cons(z0, z1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1))
   A__ULENGTH(tt, z0) -> c31(A__LENGTH(mark(z0)), MARK(z0))
   MARK(and(z0, z1)) -> c33(A__AND(mark(z0), mark(z1)), MARK(z0))
   MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, nil)) -> c28(A__ULENGTH(a__and(a__isNat(x0), tt), nil), A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__UTAKE2_4, A__LENGTH_1, A__ULENGTH_2, MARK_1, A__TAKE_2, A__ISNATLIST_1

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c26_1, c29_3, c31_2, c33_2, c34_2, c35_1, c36_1, c37_1, c38_2, c40_2, c41_2, c43_2, c44_2, c47_1, c48_1, c19_1, c42_1, c4_2, c4_1, c5_2, c5_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c15_1, c20_3, c20_2, c21_4, c21_3, c22_4, c22_3, c28_3, c28_2


----------------------------------------

(101) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__LENGTH(cons(z0, z1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(z1)), z1), A__AND(a__isNat(z0), a__isNatList(z1)), A__ISNATLIST(z1)) by 
   A__LENGTH(cons(x0, x1)) -> c29(A__ULENGTH(and(a__isNat(x0), a__isNatList(x1)), x1), A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c29(A__ULENGTH(a__and(a__isNat(x0), tt), nil), A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNATLIST(nil))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))

----------------------------------------

(102)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   A__ULENGTH(tt, z0) -> c31(A__LENGTH(mark(z0)), MARK(z0))
   MARK(and(z0, z1)) -> c33(A__AND(mark(z0), mark(z1)), MARK(z0))
   MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, nil)) -> c28(A__ULENGTH(a__and(a__isNat(x0), tt), nil), A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, x1)) -> c29(A__ULENGTH(and(a__isNat(x0), a__isNatList(x1)), x1), A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c29(A__ULENGTH(a__and(a__isNat(x0), tt), nil), A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNATLIST(nil))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   A__ULENGTH(tt, z0) -> c31(A__LENGTH(mark(z0)), MARK(z0))
   MARK(and(z0, z1)) -> c33(A__AND(mark(z0), mark(z1)), MARK(z0))
   MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, nil)) -> c28(A__ULENGTH(a__and(a__isNat(x0), tt), nil), A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, x1)) -> c29(A__ULENGTH(and(a__isNat(x0), a__isNatList(x1)), x1), A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c29(A__ULENGTH(a__and(a__isNat(x0), tt), nil), A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNATLIST(nil))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__UTAKE2_4, A__ULENGTH_2, MARK_1, A__TAKE_2, A__ISNATLIST_1, A__LENGTH_1

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c26_1, c31_2, c33_2, c34_2, c35_1, c36_1, c37_1, c38_2, c40_2, c41_2, c43_2, c44_2, c47_1, c48_1, c19_1, c42_1, c4_2, c4_1, c5_2, c5_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c15_1, c20_3, c20_2, c21_4, c21_3, c22_4, c22_3, c28_3, c28_2, c29_3


----------------------------------------

(103) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing tuple parts
----------------------------------------

(104)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   A__ULENGTH(tt, z0) -> c31(A__LENGTH(mark(z0)), MARK(z0))
   MARK(and(z0, z1)) -> c33(A__AND(mark(z0), mark(z1)), MARK(z0))
   MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, nil)) -> c28(A__ULENGTH(a__and(a__isNat(x0), tt), nil), A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c29(A__ULENGTH(a__and(a__isNat(x0), tt), nil), A__AND(a__isNat(x0), a__isNatList(nil)))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   A__ULENGTH(tt, z0) -> c31(A__LENGTH(mark(z0)), MARK(z0))
   MARK(and(z0, z1)) -> c33(A__AND(mark(z0), mark(z1)), MARK(z0))
   MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, nil)) -> c28(A__ULENGTH(a__and(a__isNat(x0), tt), nil), A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c29(A__ULENGTH(a__and(a__isNat(x0), tt), nil), A__AND(a__isNat(x0), a__isNatList(nil)))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__UTAKE2_4, A__ULENGTH_2, MARK_1, A__TAKE_2, A__ISNATLIST_1, A__LENGTH_1

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c26_1, c31_2, c33_2, c34_2, c35_1, c36_1, c37_1, c38_2, c40_2, c41_2, c43_2, c44_2, c47_1, c48_1, c19_1, c42_1, c4_2, c4_1, c5_2, c5_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c15_1, c20_3, c20_2, c21_4, c21_3, c22_4, c22_3, c28_3, c28_2, c29_3, c29_2


----------------------------------------

(105) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__ULENGTH(tt, z0) -> c31(A__LENGTH(mark(z0)), MARK(z0)) by 
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros), MARK(zeros))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, tt) -> c31(A__LENGTH(tt), MARK(tt))
   A__ULENGTH(tt, 0) -> c31(A__LENGTH(0), MARK(0))
   A__ULENGTH(tt, s(z0)) -> c31(A__LENGTH(s(mark(z0))), MARK(s(z0)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__ULENGTH(tt, nil) -> c31(A__LENGTH(nil), MARK(nil))

----------------------------------------

(106)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(and(z0, z1)) -> c33(A__AND(mark(z0), mark(z1)), MARK(z0))
   MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, nil)) -> c28(A__ULENGTH(a__and(a__isNat(x0), tt), nil), A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c29(A__ULENGTH(a__and(a__isNat(x0), tt), nil), A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros), MARK(zeros))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, tt) -> c31(A__LENGTH(tt), MARK(tt))
   A__ULENGTH(tt, 0) -> c31(A__LENGTH(0), MARK(0))
   A__ULENGTH(tt, s(z0)) -> c31(A__LENGTH(s(mark(z0))), MARK(s(z0)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__ULENGTH(tt, nil) -> c31(A__LENGTH(nil), MARK(nil))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(and(z0, z1)) -> c33(A__AND(mark(z0), mark(z1)), MARK(z0))
   MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, nil)) -> c28(A__ULENGTH(a__and(a__isNat(x0), tt), nil), A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c29(A__ULENGTH(a__and(a__isNat(x0), tt), nil), A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros), MARK(zeros))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, tt) -> c31(A__LENGTH(tt), MARK(tt))
   A__ULENGTH(tt, 0) -> c31(A__LENGTH(0), MARK(0))
   A__ULENGTH(tt, s(z0)) -> c31(A__LENGTH(s(mark(z0))), MARK(s(z0)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__ULENGTH(tt, nil) -> c31(A__LENGTH(nil), MARK(nil))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__UTAKE2_4, MARK_1, A__TAKE_2, A__ISNATLIST_1, A__LENGTH_1, A__ULENGTH_2

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c26_1, c33_2, c34_2, c35_1, c36_1, c37_1, c38_2, c40_2, c41_2, c43_2, c44_2, c47_1, c48_1, c19_1, c42_1, c4_2, c4_1, c5_2, c5_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c15_1, c20_3, c20_2, c21_4, c21_3, c22_4, c22_3, c28_3, c28_2, c29_3, c29_2, c31_2


----------------------------------------

(107) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 3 trailing nodes:
   A__ULENGTH(tt, tt) -> c31(A__LENGTH(tt), MARK(tt))
   A__ULENGTH(tt, 0) -> c31(A__LENGTH(0), MARK(0))
   A__ULENGTH(tt, nil) -> c31(A__LENGTH(nil), MARK(nil))

----------------------------------------

(108)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(and(z0, z1)) -> c33(A__AND(mark(z0), mark(z1)), MARK(z0))
   MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, nil)) -> c28(A__ULENGTH(a__and(a__isNat(x0), tt), nil), A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c29(A__ULENGTH(a__and(a__isNat(x0), tt), nil), A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros), MARK(zeros))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, s(z0)) -> c31(A__LENGTH(s(mark(z0))), MARK(s(z0)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(and(z0, z1)) -> c33(A__AND(mark(z0), mark(z1)), MARK(z0))
   MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, nil)) -> c28(A__ULENGTH(a__and(a__isNat(x0), tt), nil), A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c29(A__ULENGTH(a__and(a__isNat(x0), tt), nil), A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros), MARK(zeros))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, s(z0)) -> c31(A__LENGTH(s(mark(z0))), MARK(s(z0)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__UTAKE2_4, MARK_1, A__TAKE_2, A__ISNATLIST_1, A__LENGTH_1, A__ULENGTH_2

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c26_1, c33_2, c34_2, c35_1, c36_1, c37_1, c38_2, c40_2, c41_2, c43_2, c44_2, c47_1, c48_1, c19_1, c42_1, c4_2, c4_1, c5_2, c5_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c15_1, c20_3, c20_2, c21_4, c21_3, c22_4, c22_3, c28_3, c28_2, c29_3, c29_2, c31_2


----------------------------------------

(109) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 4 trailing tuple parts
----------------------------------------

(110)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(and(z0, z1)) -> c33(A__AND(mark(z0), mark(z1)), MARK(z0))
   MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(and(z0, z1)) -> c33(A__AND(mark(z0), mark(z1)), MARK(z0))
   MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__UTAKE2_4, MARK_1, A__TAKE_2, A__ISNATLIST_1, A__LENGTH_1, A__ULENGTH_2

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c26_1, c33_2, c34_2, c35_1, c36_1, c37_1, c38_2, c40_2, c41_2, c43_2, c44_2, c47_1, c48_1, c19_1, c42_1, c4_2, c4_1, c5_2, c5_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c15_1, c20_3, c20_2, c21_4, c21_3, c22_4, c22_3, c28_3, c28_2, c29_3, c29_2, c31_2, c29_1, c31_1


----------------------------------------

(111) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(and(z0, z1)) -> c33(A__AND(mark(z0), mark(z1)), MARK(z0)) by 
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)), MARK(zeros))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)), MARK(tt))
   MARK(and(0, x1)) -> c33(A__AND(0, mark(x1)), MARK(0))
   MARK(and(s(z0), x1)) -> c33(A__AND(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(A__AND(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1)))
   MARK(and(nil, x1)) -> c33(A__AND(nil, mark(x1)), MARK(nil))

----------------------------------------

(112)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)), MARK(zeros))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)), MARK(tt))
   MARK(and(0, x1)) -> c33(A__AND(0, mark(x1)), MARK(0))
   MARK(and(s(z0), x1)) -> c33(A__AND(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(A__AND(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1)))
   MARK(and(nil, x1)) -> c33(A__AND(nil, mark(x1)), MARK(nil))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)), MARK(zeros))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)), MARK(tt))
   MARK(and(0, x1)) -> c33(A__AND(0, mark(x1)), MARK(0))
   MARK(and(s(z0), x1)) -> c33(A__AND(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(A__AND(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1)))
   MARK(and(nil, x1)) -> c33(A__AND(nil, mark(x1)), MARK(nil))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__UTAKE2_4, MARK_1, A__TAKE_2, A__ISNATLIST_1, A__LENGTH_1, A__ULENGTH_2

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c26_1, c34_2, c35_1, c36_1, c37_1, c38_2, c40_2, c41_2, c43_2, c44_2, c47_1, c48_1, c19_1, c42_1, c4_2, c4_1, c5_2, c5_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c15_1, c20_3, c20_2, c21_4, c21_3, c22_4, c22_3, c28_3, c28_2, c29_3, c29_2, c31_2, c29_1, c31_1, c33_2


----------------------------------------

(113) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing nodes:
   MARK(and(0, x1)) -> c33(A__AND(0, mark(x1)), MARK(0))
   MARK(and(nil, x1)) -> c33(A__AND(nil, mark(x1)), MARK(nil))

----------------------------------------

(114)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)), MARK(zeros))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)), MARK(tt))
   MARK(and(s(z0), x1)) -> c33(A__AND(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(A__AND(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1)))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)), MARK(zeros))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)), MARK(tt))
   MARK(and(s(z0), x1)) -> c33(A__AND(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(A__AND(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1)))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__UTAKE2_4, MARK_1, A__TAKE_2, A__ISNATLIST_1, A__LENGTH_1, A__ULENGTH_2

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c26_1, c34_2, c35_1, c36_1, c37_1, c38_2, c40_2, c41_2, c43_2, c44_2, c47_1, c48_1, c19_1, c42_1, c4_2, c4_1, c5_2, c5_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c15_1, c20_3, c20_2, c21_4, c21_3, c22_4, c22_3, c28_3, c28_2, c29_3, c29_2, c31_2, c29_1, c31_1, c33_2


----------------------------------------

(115) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 4 trailing tuple parts
----------------------------------------

(116)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__UTAKE2_4, MARK_1, A__TAKE_2, A__ISNATLIST_1, A__LENGTH_1, A__ULENGTH_2

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c26_1, c34_2, c35_1, c36_1, c37_1, c38_2, c40_2, c41_2, c43_2, c44_2, c47_1, c48_1, c19_1, c42_1, c4_2, c4_1, c5_2, c5_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c15_1, c20_3, c20_2, c21_4, c21_3, c22_4, c22_3, c28_3, c28_2, c29_3, c29_2, c31_2, c29_1, c31_1, c33_2, c33_1


----------------------------------------

(117) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(and(z0, z1)) -> c34(A__AND(mark(z0), mark(z1)), MARK(z1)) by 
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros), MARK(zeros))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt), MARK(tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0), MARK(0))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil), MARK(nil))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(0, x1)) -> c34(A__AND(0, mark(x1)), MARK(x1))
   MARK(and(s(z0), x1)) -> c34(A__AND(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(A__AND(cons(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(nil, x1)) -> c34(A__AND(nil, mark(x1)), MARK(x1))

----------------------------------------

(118)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros), MARK(zeros))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt), MARK(tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0), MARK(0))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil), MARK(nil))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(0, x1)) -> c34(A__AND(0, mark(x1)), MARK(x1))
   MARK(and(s(z0), x1)) -> c34(A__AND(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(A__AND(cons(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(nil, x1)) -> c34(A__AND(nil, mark(x1)), MARK(x1))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros), MARK(zeros))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt), MARK(tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0), MARK(0))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil), MARK(nil))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(0, x1)) -> c34(A__AND(0, mark(x1)), MARK(x1))
   MARK(and(s(z0), x1)) -> c34(A__AND(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(A__AND(cons(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(nil, x1)) -> c34(A__AND(nil, mark(x1)), MARK(x1))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__UTAKE2_4, MARK_1, A__TAKE_2, A__ISNATLIST_1, A__LENGTH_1, A__ULENGTH_2

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c26_1, c35_1, c36_1, c37_1, c38_2, c40_2, c41_2, c43_2, c44_2, c47_1, c48_1, c19_1, c42_1, c4_2, c4_1, c5_2, c5_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c15_1, c20_3, c20_2, c21_4, c21_3, c22_4, c22_3, c28_3, c28_2, c29_3, c29_2, c31_2, c29_1, c31_1, c33_2, c33_1, c34_2


----------------------------------------

(119) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 8 trailing tuple parts
----------------------------------------

(120)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0))
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__UTAKE2_4, MARK_1, A__TAKE_2, A__ISNATLIST_1, A__LENGTH_1, A__ULENGTH_2

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c26_1, c35_1, c36_1, c37_1, c38_2, c40_2, c41_2, c43_2, c44_2, c47_1, c48_1, c19_1, c42_1, c4_2, c4_1, c5_2, c5_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c15_1, c20_3, c20_2, c21_4, c21_3, c22_4, c22_3, c28_3, c28_2, c29_3, c29_2, c31_2, c29_1, c31_1, c33_2, c33_1, c34_2, c34_1


----------------------------------------

(121) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(length(z0)) -> c38(A__LENGTH(mark(z0)), MARK(z0)) by 
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros), MARK(zeros))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(tt)) -> c38(A__LENGTH(tt), MARK(tt))
   MARK(length(0)) -> c38(A__LENGTH(0), MARK(0))
   MARK(length(s(z0))) -> c38(A__LENGTH(s(mark(z0))), MARK(s(z0)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(nil)) -> c38(A__LENGTH(nil), MARK(nil))

----------------------------------------

(122)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros), MARK(zeros))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(tt)) -> c38(A__LENGTH(tt), MARK(tt))
   MARK(length(0)) -> c38(A__LENGTH(0), MARK(0))
   MARK(length(s(z0))) -> c38(A__LENGTH(s(mark(z0))), MARK(s(z0)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(nil)) -> c38(A__LENGTH(nil), MARK(nil))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros), MARK(zeros))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(tt)) -> c38(A__LENGTH(tt), MARK(tt))
   MARK(length(0)) -> c38(A__LENGTH(0), MARK(0))
   MARK(length(s(z0))) -> c38(A__LENGTH(s(mark(z0))), MARK(s(z0)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(nil)) -> c38(A__LENGTH(nil), MARK(nil))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__UTAKE2_4, MARK_1, A__TAKE_2, A__ISNATLIST_1, A__LENGTH_1, A__ULENGTH_2

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c26_1, c35_1, c36_1, c37_1, c40_2, c41_2, c43_2, c44_2, c47_1, c48_1, c19_1, c42_1, c4_2, c4_1, c5_2, c5_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c15_1, c20_3, c20_2, c21_4, c21_3, c22_4, c22_3, c28_3, c28_2, c29_3, c29_2, c31_2, c29_1, c31_1, c33_2, c33_1, c34_2, c34_1, c38_2


----------------------------------------

(123) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 3 trailing nodes:
   MARK(length(tt)) -> c38(A__LENGTH(tt), MARK(tt))
   MARK(length(nil)) -> c38(A__LENGTH(nil), MARK(nil))
   MARK(length(0)) -> c38(A__LENGTH(0), MARK(0))

----------------------------------------

(124)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros), MARK(zeros))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(s(z0))) -> c38(A__LENGTH(s(mark(z0))), MARK(s(z0)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros), MARK(zeros))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(s(z0))) -> c38(A__LENGTH(s(mark(z0))), MARK(s(z0)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__UTAKE2_4, MARK_1, A__TAKE_2, A__ISNATLIST_1, A__LENGTH_1, A__ULENGTH_2

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c26_1, c35_1, c36_1, c37_1, c40_2, c41_2, c43_2, c44_2, c47_1, c48_1, c19_1, c42_1, c4_2, c4_1, c5_2, c5_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c15_1, c20_3, c20_2, c21_4, c21_3, c22_4, c22_3, c28_3, c28_2, c29_3, c29_2, c31_2, c29_1, c31_1, c33_2, c33_1, c34_2, c34_1, c38_2


----------------------------------------

(125) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing tuple parts
----------------------------------------

(126)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__UTAKE2_4, MARK_1, A__TAKE_2, A__ISNATLIST_1, A__LENGTH_1, A__ULENGTH_2

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c26_1, c35_1, c36_1, c37_1, c40_2, c41_2, c43_2, c44_2, c47_1, c48_1, c19_1, c42_1, c4_2, c4_1, c5_2, c5_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c15_1, c20_3, c20_2, c21_4, c21_3, c22_4, c22_3, c28_3, c28_2, c29_3, c29_2, c31_2, c29_1, c31_1, c33_2, c33_1, c34_2, c34_1, c38_2, c38_1


----------------------------------------

(127) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(take(z0, z1)) -> c40(A__TAKE(mark(z0), mark(z1)), MARK(z0)) by 
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)), MARK(zeros))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(tt, x1)) -> c40(A__TAKE(tt, mark(x1)), MARK(tt))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)), MARK(0))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(cons(z0, z1), x1)) -> c40(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1)))
   MARK(take(nil, x1)) -> c40(A__TAKE(nil, mark(x1)), MARK(nil))

----------------------------------------

(128)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)), MARK(zeros))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(tt, x1)) -> c40(A__TAKE(tt, mark(x1)), MARK(tt))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)), MARK(0))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(cons(z0, z1), x1)) -> c40(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1)))
   MARK(take(nil, x1)) -> c40(A__TAKE(nil, mark(x1)), MARK(nil))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)), MARK(zeros))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(tt, x1)) -> c40(A__TAKE(tt, mark(x1)), MARK(tt))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)), MARK(0))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(cons(z0, z1), x1)) -> c40(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1)))
   MARK(take(nil, x1)) -> c40(A__TAKE(nil, mark(x1)), MARK(nil))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__UTAKE2_4, MARK_1, A__TAKE_2, A__ISNATLIST_1, A__LENGTH_1, A__ULENGTH_2

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c26_1, c35_1, c36_1, c37_1, c41_2, c43_2, c44_2, c47_1, c48_1, c19_1, c42_1, c4_2, c4_1, c5_2, c5_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c15_1, c20_3, c20_2, c21_4, c21_3, c22_4, c22_3, c28_3, c28_2, c29_3, c29_2, c31_2, c29_1, c31_1, c33_2, c33_1, c34_2, c34_1, c38_2, c38_1, c40_2


----------------------------------------

(129) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing nodes:
   MARK(take(tt, x1)) -> c40(A__TAKE(tt, mark(x1)), MARK(tt))
   MARK(take(nil, x1)) -> c40(A__TAKE(nil, mark(x1)), MARK(nil))

----------------------------------------

(130)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)), MARK(zeros))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)), MARK(0))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(cons(z0, z1), x1)) -> c40(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1)))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)), MARK(zeros))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)), MARK(0))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(cons(z0, z1), x1)) -> c40(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1)))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__UTAKE2_4, MARK_1, A__TAKE_2, A__ISNATLIST_1, A__LENGTH_1, A__ULENGTH_2

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c26_1, c35_1, c36_1, c37_1, c41_2, c43_2, c44_2, c47_1, c48_1, c19_1, c42_1, c4_2, c4_1, c5_2, c5_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c15_1, c20_3, c20_2, c21_4, c21_3, c22_4, c22_3, c28_3, c28_2, c29_3, c29_2, c31_2, c29_1, c31_1, c33_2, c33_1, c34_2, c34_1, c38_2, c38_1, c40_2


----------------------------------------

(131) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 3 trailing tuple parts
----------------------------------------

(132)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__UTAKE2_4, MARK_1, A__TAKE_2, A__ISNATLIST_1, A__LENGTH_1, A__ULENGTH_2

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c26_1, c35_1, c36_1, c37_1, c41_2, c43_2, c44_2, c47_1, c48_1, c19_1, c42_1, c4_2, c4_1, c5_2, c5_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c15_1, c20_3, c20_2, c21_4, c21_3, c22_4, c22_3, c28_3, c28_2, c29_3, c29_2, c31_2, c29_1, c31_1, c33_2, c33_1, c34_2, c34_1, c38_2, c38_1, c40_2, c40_1


----------------------------------------

(133) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(take(z0, z1)) -> c41(A__TAKE(mark(z0), mark(z1)), MARK(z1)) by 
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros), MARK(zeros))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt), MARK(tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0), MARK(0))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil), MARK(nil))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(tt, x1)) -> c41(A__TAKE(tt, mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(nil, x1)) -> c41(A__TAKE(nil, mark(x1)), MARK(x1))

----------------------------------------

(134)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros), MARK(zeros))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt), MARK(tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0), MARK(0))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil), MARK(nil))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(tt, x1)) -> c41(A__TAKE(tt, mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(nil, x1)) -> c41(A__TAKE(nil, mark(x1)), MARK(x1))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros), MARK(zeros))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt), MARK(tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0), MARK(0))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil), MARK(nil))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(tt, x1)) -> c41(A__TAKE(tt, mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(nil, x1)) -> c41(A__TAKE(nil, mark(x1)), MARK(x1))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__UTAKE2_4, MARK_1, A__TAKE_2, A__ISNATLIST_1, A__LENGTH_1, A__ULENGTH_2

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c26_1, c35_1, c36_1, c37_1, c43_2, c44_2, c47_1, c48_1, c19_1, c42_1, c4_2, c4_1, c5_2, c5_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c15_1, c20_3, c20_2, c21_4, c21_3, c22_4, c22_3, c28_3, c28_2, c29_3, c29_2, c31_2, c29_1, c31_1, c33_2, c33_1, c34_2, c34_1, c38_2, c38_1, c40_2, c40_1, c41_2


----------------------------------------

(135) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 7 trailing tuple parts
----------------------------------------

(136)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__UTAKE2_4, MARK_1, A__TAKE_2, A__ISNATLIST_1, A__LENGTH_1, A__ULENGTH_2

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c26_1, c35_1, c36_1, c37_1, c43_2, c44_2, c47_1, c48_1, c19_1, c42_1, c4_2, c4_1, c5_2, c5_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c15_1, c20_3, c20_2, c21_4, c21_3, c22_4, c22_3, c28_3, c28_2, c29_3, c29_2, c31_2, c29_1, c31_1, c33_2, c33_1, c34_2, c34_1, c38_2, c38_1, c40_2, c40_1, c41_2, c41_1


----------------------------------------

(137) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(uTake2(z0, z1, z2, z3)) -> c43(A__UTAKE2(mark(z0), z1, z2, z3), MARK(z0)) by 
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3), MARK(zeros))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3), MARK(tt))
   MARK(uTake2(0, x1, x2, x3)) -> c43(A__UTAKE2(0, x1, x2, x3), MARK(0))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(A__UTAKE2(s(mark(z0)), x1, x2, x3), MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(cons(mark(z0), z1), x1, x2, x3), MARK(cons(z0, z1)))
   MARK(uTake2(nil, x1, x2, x3)) -> c43(A__UTAKE2(nil, x1, x2, x3), MARK(nil))

----------------------------------------

(138)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3), MARK(zeros))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3), MARK(tt))
   MARK(uTake2(0, x1, x2, x3)) -> c43(A__UTAKE2(0, x1, x2, x3), MARK(0))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(A__UTAKE2(s(mark(z0)), x1, x2, x3), MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(cons(mark(z0), z1), x1, x2, x3), MARK(cons(z0, z1)))
   MARK(uTake2(nil, x1, x2, x3)) -> c43(A__UTAKE2(nil, x1, x2, x3), MARK(nil))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3), MARK(zeros))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3), MARK(tt))
   MARK(uTake2(0, x1, x2, x3)) -> c43(A__UTAKE2(0, x1, x2, x3), MARK(0))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(A__UTAKE2(s(mark(z0)), x1, x2, x3), MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(cons(mark(z0), z1), x1, x2, x3), MARK(cons(z0, z1)))
   MARK(uTake2(nil, x1, x2, x3)) -> c43(A__UTAKE2(nil, x1, x2, x3), MARK(nil))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__UTAKE2_4, MARK_1, A__TAKE_2, A__ISNATLIST_1, A__LENGTH_1, A__ULENGTH_2

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c26_1, c35_1, c36_1, c37_1, c44_2, c47_1, c48_1, c19_1, c42_1, c4_2, c4_1, c5_2, c5_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c15_1, c20_3, c20_2, c21_4, c21_3, c22_4, c22_3, c28_3, c28_2, c29_3, c29_2, c31_2, c29_1, c31_1, c33_2, c33_1, c34_2, c34_1, c38_2, c38_1, c40_2, c40_1, c41_2, c41_1, c43_2


----------------------------------------

(139) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing nodes:
   MARK(uTake2(0, x1, x2, x3)) -> c43(A__UTAKE2(0, x1, x2, x3), MARK(0))
   MARK(uTake2(nil, x1, x2, x3)) -> c43(A__UTAKE2(nil, x1, x2, x3), MARK(nil))

----------------------------------------

(140)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3), MARK(zeros))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3), MARK(tt))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(A__UTAKE2(s(mark(z0)), x1, x2, x3), MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(cons(mark(z0), z1), x1, x2, x3), MARK(cons(z0, z1)))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3), MARK(zeros))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3), MARK(tt))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(A__UTAKE2(s(mark(z0)), x1, x2, x3), MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(cons(mark(z0), z1), x1, x2, x3), MARK(cons(z0, z1)))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__UTAKE2_4, MARK_1, A__TAKE_2, A__ISNATLIST_1, A__LENGTH_1, A__ULENGTH_2

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c26_1, c35_1, c36_1, c37_1, c44_2, c47_1, c48_1, c19_1, c42_1, c4_2, c4_1, c5_2, c5_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c15_1, c20_3, c20_2, c21_4, c21_3, c22_4, c22_3, c28_3, c28_2, c29_3, c29_2, c31_2, c29_1, c31_1, c33_2, c33_1, c34_2, c34_1, c38_2, c38_1, c40_2, c40_1, c41_2, c41_1, c43_2


----------------------------------------

(141) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 4 trailing tuple parts
----------------------------------------

(142)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__UTAKE2_4, MARK_1, A__TAKE_2, A__ISNATLIST_1, A__LENGTH_1, A__ULENGTH_2

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c26_1, c35_1, c36_1, c37_1, c44_2, c47_1, c48_1, c19_1, c42_1, c4_2, c4_1, c5_2, c5_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c15_1, c20_3, c20_2, c21_4, c21_3, c22_4, c22_3, c28_3, c28_2, c29_3, c29_2, c31_2, c29_1, c31_1, c33_2, c33_1, c34_2, c34_1, c38_2, c38_1, c40_2, c40_1, c41_2, c41_1, c43_2, c43_1


----------------------------------------

(143) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(uLength(z0, z1)) -> c44(A__ULENGTH(mark(z0), z1), MARK(z0)) by 
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1), MARK(zeros))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1), MARK(tt))
   MARK(uLength(0, x1)) -> c44(A__ULENGTH(0, x1), MARK(0))
   MARK(uLength(s(z0), x1)) -> c44(A__ULENGTH(s(mark(z0)), x1), MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(A__ULENGTH(cons(mark(z0), z1), x1), MARK(cons(z0, z1)))
   MARK(uLength(nil, x1)) -> c44(A__ULENGTH(nil, x1), MARK(nil))

----------------------------------------

(144)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1), MARK(zeros))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1), MARK(tt))
   MARK(uLength(0, x1)) -> c44(A__ULENGTH(0, x1), MARK(0))
   MARK(uLength(s(z0), x1)) -> c44(A__ULENGTH(s(mark(z0)), x1), MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(A__ULENGTH(cons(mark(z0), z1), x1), MARK(cons(z0, z1)))
   MARK(uLength(nil, x1)) -> c44(A__ULENGTH(nil, x1), MARK(nil))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1), MARK(zeros))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1), MARK(tt))
   MARK(uLength(0, x1)) -> c44(A__ULENGTH(0, x1), MARK(0))
   MARK(uLength(s(z0), x1)) -> c44(A__ULENGTH(s(mark(z0)), x1), MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(A__ULENGTH(cons(mark(z0), z1), x1), MARK(cons(z0, z1)))
   MARK(uLength(nil, x1)) -> c44(A__ULENGTH(nil, x1), MARK(nil))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__UTAKE2_4, MARK_1, A__TAKE_2, A__ISNATLIST_1, A__LENGTH_1, A__ULENGTH_2

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c26_1, c35_1, c36_1, c37_1, c47_1, c48_1, c19_1, c42_1, c4_2, c4_1, c5_2, c5_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c15_1, c20_3, c20_2, c21_4, c21_3, c22_4, c22_3, c28_3, c28_2, c29_3, c29_2, c31_2, c29_1, c31_1, c33_2, c33_1, c34_2, c34_1, c38_2, c38_1, c40_2, c40_1, c41_2, c41_1, c43_2, c43_1, c44_2


----------------------------------------

(145) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing nodes:
   MARK(uLength(nil, x1)) -> c44(A__ULENGTH(nil, x1), MARK(nil))
   MARK(uLength(0, x1)) -> c44(A__ULENGTH(0, x1), MARK(0))

----------------------------------------

(146)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1), MARK(zeros))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1), MARK(tt))
   MARK(uLength(s(z0), x1)) -> c44(A__ULENGTH(s(mark(z0)), x1), MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(A__ULENGTH(cons(mark(z0), z1), x1), MARK(cons(z0, z1)))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1), MARK(zeros))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1), MARK(tt))
   MARK(uLength(s(z0), x1)) -> c44(A__ULENGTH(s(mark(z0)), x1), MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(A__ULENGTH(cons(mark(z0), z1), x1), MARK(cons(z0, z1)))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__UTAKE2_4, MARK_1, A__TAKE_2, A__ISNATLIST_1, A__LENGTH_1, A__ULENGTH_2

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c26_1, c35_1, c36_1, c37_1, c47_1, c48_1, c19_1, c42_1, c4_2, c4_1, c5_2, c5_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c15_1, c20_3, c20_2, c21_4, c21_3, c22_4, c22_3, c28_3, c28_2, c29_3, c29_2, c31_2, c29_1, c31_1, c33_2, c33_1, c34_2, c34_1, c38_2, c38_1, c40_2, c40_1, c41_2, c41_1, c43_2, c43_1, c44_2


----------------------------------------

(147) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 4 trailing tuple parts
----------------------------------------

(148)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__UTAKE2_4, MARK_1, A__TAKE_2, A__ISNATLIST_1, A__LENGTH_1, A__ULENGTH_2

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c26_1, c35_1, c36_1, c37_1, c47_1, c48_1, c19_1, c42_1, c4_2, c4_1, c5_2, c5_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c15_1, c20_3, c20_2, c21_4, c21_3, c22_4, c22_3, c28_3, c28_2, c29_3, c29_2, c31_2, c29_1, c31_1, c33_2, c33_1, c34_2, c34_1, c38_2, c38_1, c40_2, c40_1, c41_2, c41_1, c43_2, c43_1, c44_2, c44_1


----------------------------------------

(149) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0)) by 
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)), A__ISNAT(0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__AND(isNat(z0), a__isNatList(x1)), A__ISNAT(z0))

----------------------------------------

(150)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)), A__ISNAT(0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__AND(isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)), A__ISNAT(0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__AND(isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__UTAKE2_4, MARK_1, A__TAKE_2, A__ISNATLIST_1, A__LENGTH_1, A__ULENGTH_2

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c26_1, c35_1, c36_1, c37_1, c47_1, c48_1, c19_1, c42_1, c4_2, c4_1, c5_2, c5_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c15_1, c20_3, c20_2, c21_4, c21_3, c22_4, c22_3, c28_3, c28_2, c29_3, c29_2, c31_2, c29_1, c31_1, c33_2, c33_1, c34_2, c34_1, c38_2, c38_1, c40_2, c40_1, c41_2, c41_1, c43_2, c43_1, c44_2, c44_1


----------------------------------------

(151) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing tuple parts
----------------------------------------

(152)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__UTAKE2_4, MARK_1, A__TAKE_2, A__ISNATLIST_1, A__LENGTH_1, A__ULENGTH_2

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c26_1, c35_1, c36_1, c37_1, c47_1, c48_1, c19_1, c42_1, c4_2, c4_1, c5_2, c5_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c15_1, c20_3, c20_2, c21_4, c21_3, c22_4, c22_3, c28_3, c28_2, c29_3, c29_2, c31_2, c29_1, c31_1, c33_2, c33_1, c34_2, c34_1, c38_2, c38_1, c40_2, c40_1, c41_2, c41_1, c43_2, c43_1, c44_2, c44_1


----------------------------------------

(153) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__ISNATILIST(cons(x0, zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0)) by 
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt), A__ISNAT(0))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__AND(isNat(z0), tt), A__ISNAT(z0))

----------------------------------------

(154)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt), A__ISNAT(0))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__AND(isNat(z0), tt), A__ISNAT(z0))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt), A__ISNAT(0))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__AND(isNat(z0), tt), A__ISNAT(z0))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__UTAKE2_4, MARK_1, A__TAKE_2, A__ISNATLIST_1, A__LENGTH_1, A__ULENGTH_2

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c26_1, c35_1, c36_1, c37_1, c47_1, c48_1, c19_1, c42_1, c4_2, c4_1, c5_2, c5_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c15_1, c20_3, c20_2, c21_4, c21_3, c22_4, c22_3, c28_3, c28_2, c29_3, c29_2, c31_2, c29_1, c31_1, c33_2, c33_1, c34_2, c34_1, c38_2, c38_1, c40_2, c40_1, c41_2, c41_1, c43_2, c43_1, c44_2, c44_1


----------------------------------------

(155) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing tuple parts
----------------------------------------

(156)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__UTAKE2_4, MARK_1, A__TAKE_2, A__ISNATLIST_1, A__LENGTH_1, A__ULENGTH_2

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c26_1, c35_1, c36_1, c37_1, c47_1, c48_1, c19_1, c42_1, c4_2, c4_1, c5_2, c5_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c15_1, c20_3, c20_2, c21_4, c21_3, c22_4, c22_3, c28_3, c28_2, c29_3, c29_2, c31_2, c29_1, c31_1, c33_2, c33_1, c34_2, c34_1, c38_2, c38_1, c40_2, c40_1, c41_2, c41_1, c43_2, c43_1, c44_2, c44_1


----------------------------------------

(157) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0)) by 
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__AND(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))

----------------------------------------

(158)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__AND(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__AND(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__UTAKE2_4, MARK_1, A__TAKE_2, A__ISNATLIST_1, A__LENGTH_1, A__ULENGTH_2

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c26_1, c35_1, c36_1, c37_1, c47_1, c48_1, c19_1, c42_1, c4_2, c4_1, c5_2, c5_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c15_1, c20_3, c20_2, c21_4, c21_3, c22_4, c22_3, c28_3, c28_2, c29_3, c29_2, c31_2, c29_1, c31_1, c33_2, c33_1, c34_2, c34_1, c38_2, c38_1, c40_2, c40_1, c41_2, c41_1, c43_2, c43_1, c44_2, c44_1


----------------------------------------

(159) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing tuple parts
----------------------------------------

(160)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__ISNAT(z0))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__ISNAT(z0))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__UTAKE2_4, MARK_1, A__TAKE_2, A__ISNATLIST_1, A__LENGTH_1, A__ULENGTH_2

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c26_1, c35_1, c36_1, c37_1, c47_1, c48_1, c19_1, c42_1, c4_2, c4_1, c5_2, c5_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c15_1, c20_3, c20_2, c21_4, c21_3, c22_4, c22_3, c28_3, c28_2, c29_3, c29_2, c31_2, c29_1, c31_1, c33_2, c33_1, c34_2, c34_1, c38_2, c38_1, c40_2, c40_1, c41_2, c41_1, c43_2, c43_1, c44_2, c44_1


----------------------------------------

(161) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0)) by 
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, isNatIList(x1)), A__ISNAT(0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__AND(isNat(z0), isNatIList(x1)), A__ISNAT(z0))

----------------------------------------

(162)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, isNatIList(x1)), A__ISNAT(0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__AND(isNat(z0), isNatIList(x1)), A__ISNAT(z0))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, isNatIList(x1)), A__ISNAT(0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__AND(isNat(z0), isNatIList(x1)), A__ISNAT(z0))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__UTAKE2_4, MARK_1, A__TAKE_2, A__ISNATLIST_1, A__LENGTH_1, A__ULENGTH_2

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c26_1, c35_1, c36_1, c37_1, c47_1, c48_1, c19_1, c42_1, c4_2, c4_1, c5_2, c5_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c15_1, c20_3, c20_2, c21_4, c21_3, c22_4, c22_3, c28_3, c28_2, c29_3, c29_2, c31_2, c29_1, c31_1, c33_2, c33_1, c34_2, c34_1, c38_2, c38_1, c40_2, c40_1, c41_2, c41_1, c43_2, c43_1, c44_2, c44_1


----------------------------------------

(163) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing tuple parts
----------------------------------------

(164)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, isNatIList(x1)))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, isNatIList(x1)))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__UTAKE2_4, MARK_1, A__TAKE_2, A__ISNATLIST_1, A__LENGTH_1, A__ULENGTH_2

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c26_1, c35_1, c36_1, c37_1, c47_1, c48_1, c19_1, c42_1, c4_2, c4_1, c5_2, c5_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c15_1, c20_3, c20_2, c21_4, c21_3, c22_4, c22_3, c28_3, c28_2, c29_3, c29_2, c31_2, c29_1, c31_1, c33_2, c33_1, c34_2, c34_1, c38_2, c38_1, c40_2, c40_1, c41_2, c41_1, c43_2, c43_1, c44_2, c44_1


----------------------------------------

(165) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0))) by 
   A__ISNATILIST(cons(s(x0), z0)) -> c4(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(s(x0)))
   A__ISNATILIST(cons(s(x0), zeros)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(s(x0)))
   A__ISNATILIST(cons(s(x0), cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(s(x0)))
   A__ISNATILIST(cons(s(x0), z0)) -> c4(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(s(x0)))
   A__ISNATILIST(cons(s(0), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(s(0)))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))

----------------------------------------

(166)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, isNatIList(x1)))
   A__ISNATILIST(cons(s(0), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(s(0)))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, isNatIList(x1)))
   A__ISNATILIST(cons(s(0), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(s(0)))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__UTAKE2_4, MARK_1, A__TAKE_2, A__ISNATLIST_1, A__LENGTH_1, A__ULENGTH_2

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c26_1, c35_1, c36_1, c37_1, c47_1, c48_1, c19_1, c42_1, c4_2, c4_1, c5_2, c5_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c15_1, c20_3, c20_2, c21_4, c21_3, c22_4, c22_3, c28_3, c28_2, c29_3, c29_2, c31_2, c29_1, c31_1, c33_2, c33_1, c34_2, c34_1, c38_2, c38_1, c40_2, c40_1, c41_2, c41_1, c43_2, c43_1, c44_2, c44_1


----------------------------------------

(167) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing tuple parts
----------------------------------------

(168)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, isNatIList(x1)))
   A__ISNATILIST(cons(s(0), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(s(0)))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__ISNAT(s(z0)))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, isNatIList(x1)))
   A__ISNATILIST(cons(s(0), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(s(0)))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__ISNAT(s(z0)))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__UTAKE2_4, MARK_1, A__TAKE_2, A__ISNATLIST_1, A__LENGTH_1, A__ULENGTH_2

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c26_1, c35_1, c36_1, c37_1, c47_1, c48_1, c19_1, c42_1, c4_2, c4_1, c5_2, c5_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c15_1, c20_3, c20_2, c21_4, c21_3, c22_4, c22_3, c28_3, c28_2, c29_3, c29_2, c31_2, c29_1, c31_1, c33_2, c33_1, c34_2, c34_1, c38_2, c38_1, c40_2, c40_1, c41_2, c41_1, c43_2, c43_1, c44_2, c44_1


----------------------------------------

(169) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0))) by 
   A__ISNATILIST(cons(length(x0), z0)) -> c4(A__AND(a__isNatList(x0), a__isNatList(z0)), A__ISNAT(length(x0)))
   A__ISNATILIST(cons(length(x0), zeros)) -> c4(A__AND(a__isNatList(x0), tt), A__ISNAT(length(x0)))
   A__ISNATILIST(cons(length(x0), cons(z0, z1))) -> c4(A__AND(a__isNatList(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(length(x0)))
   A__ISNATILIST(cons(length(x0), z0)) -> c4(A__AND(a__isNatList(x0), isNatIList(z0)), A__ISNAT(length(x0)))
   A__ISNATILIST(cons(length(nil), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(length(nil)))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))

----------------------------------------

(170)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, isNatIList(x1)))
   A__ISNATILIST(cons(s(0), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(s(0)))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(nil), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(length(nil)))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, isNatIList(x1)))
   A__ISNATILIST(cons(s(0), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(s(0)))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(nil), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(length(nil)))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__UTAKE2_4, MARK_1, A__TAKE_2, A__ISNATLIST_1, A__LENGTH_1, A__ULENGTH_2

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c26_1, c35_1, c36_1, c37_1, c47_1, c48_1, c19_1, c42_1, c4_1, c5_2, c5_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c15_1, c20_3, c20_2, c21_4, c21_3, c22_4, c22_3, c28_3, c28_2, c29_3, c29_2, c31_2, c29_1, c31_1, c33_2, c33_1, c34_2, c34_1, c38_2, c38_1, c40_2, c40_1, c41_2, c41_1, c43_2, c43_1, c44_2, c44_1, c4_2


----------------------------------------

(171) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing tuple parts
----------------------------------------

(172)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, isNatIList(x1)))
   A__ISNATILIST(cons(s(0), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(s(0)))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(nil), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(length(nil)))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__ISNAT(length(z0)))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1)))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, isNatIList(x1)))
   A__ISNATILIST(cons(s(0), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(s(0)))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(nil), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(length(nil)))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__ISNAT(length(z0)))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__UTAKE2_4, MARK_1, A__TAKE_2, A__ISNATLIST_1, A__LENGTH_1, A__ULENGTH_2

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c26_1, c35_1, c36_1, c37_1, c47_1, c48_1, c19_1, c42_1, c4_1, c5_2, c5_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c15_1, c20_3, c20_2, c21_4, c21_3, c22_4, c22_3, c28_3, c28_2, c29_3, c29_2, c31_2, c29_1, c31_1, c33_2, c33_1, c34_2, c34_1, c38_2, c38_1, c40_2, c40_1, c41_2, c41_1, c43_2, c43_1, c44_2, c44_1, c4_2


----------------------------------------

(173) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatIList(x1))) by 
   A__ISNATILIST(cons(0, z0)) -> c4(A__AND(tt, a__isNatList(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(0, cons(z0, z1))) -> c4(A__AND(tt, a__and(a__isNat(z0), a__isNatIList(z1))))
   A__ISNATILIST(cons(0, z0)) -> c4(A__AND(tt, isNatIList(z0)))

----------------------------------------

(174)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, isNatIList(x1)))
   A__ISNATILIST(cons(s(0), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(s(0)))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(nil), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(length(nil)))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__ISNAT(length(z0)))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, isNatIList(x1)))
   A__ISNATILIST(cons(s(0), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(s(0)))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(nil), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(length(nil)))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__ISNAT(length(z0)))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__UTAKE2_4, MARK_1, A__TAKE_2, A__ISNATLIST_1, A__LENGTH_1, A__ULENGTH_2

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c26_1, c35_1, c36_1, c37_1, c47_1, c48_1, c19_1, c42_1, c4_1, c5_2, c5_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c15_1, c20_3, c20_2, c21_4, c21_3, c22_4, c22_3, c28_3, c28_2, c29_3, c29_2, c31_2, c29_1, c31_1, c33_2, c33_1, c34_2, c34_1, c38_2, c38_1, c40_2, c40_1, c41_2, c41_1, c43_2, c43_1, c44_2, c44_1, c4_2


----------------------------------------

(175) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0)) by 
   A__ISNATILIST(cons(x0, nil)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(nil))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(take(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__AND(isNat(z0), a__isNatList(x1)), A__ISNATILIST(x1))

----------------------------------------

(176)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, isNatIList(x1)))
   A__ISNATILIST(cons(s(0), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(s(0)))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(nil), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(length(nil)))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__ISNAT(length(z0)))
   A__ISNATILIST(cons(x0, nil)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(nil))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(take(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__AND(isNat(z0), a__isNatList(x1)), A__ISNATILIST(x1))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, isNatIList(x1)))
   A__ISNATILIST(cons(s(0), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(s(0)))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(nil), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(length(nil)))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__ISNAT(length(z0)))
   A__ISNATILIST(cons(x0, nil)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(nil))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(take(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__AND(isNat(z0), a__isNatList(x1)), A__ISNATILIST(x1))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__UTAKE2_4, MARK_1, A__TAKE_2, A__ISNATLIST_1, A__LENGTH_1, A__ULENGTH_2

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c26_1, c35_1, c36_1, c37_1, c47_1, c48_1, c19_1, c42_1, c4_1, c5_2, c5_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c15_1, c20_3, c20_2, c21_4, c21_3, c22_4, c22_3, c28_3, c28_2, c29_3, c29_2, c31_2, c29_1, c31_1, c33_2, c33_1, c34_2, c34_1, c38_2, c38_1, c40_2, c40_1, c41_2, c41_1, c43_2, c43_1, c44_2, c44_1, c4_2


----------------------------------------

(177) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing tuple parts
----------------------------------------

(178)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, isNatIList(x1)))
   A__ISNATILIST(cons(s(0), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(s(0)))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(nil), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(length(nil)))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__ISNAT(length(z0)))
   A__ISNATILIST(cons(x0, nil)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(nil))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(take(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATILIST(x1))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, isNatIList(x1)))
   A__ISNATILIST(cons(s(0), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(s(0)))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(nil), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(length(nil)))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__ISNAT(length(z0)))
   A__ISNATILIST(cons(x0, nil)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(nil))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(take(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATILIST(x1))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__UTAKE2_4, MARK_1, A__TAKE_2, A__ISNATLIST_1, A__LENGTH_1, A__ULENGTH_2

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c26_1, c35_1, c36_1, c37_1, c47_1, c48_1, c19_1, c42_1, c4_1, c5_2, c5_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c15_1, c20_3, c20_2, c21_4, c21_3, c22_4, c22_3, c28_3, c28_2, c29_3, c29_2, c31_2, c29_1, c31_1, c33_2, c33_1, c34_2, c34_1, c38_2, c38_1, c40_2, c40_1, c41_2, c41_1, c43_2, c43_1, c44_2, c44_1, c4_2


----------------------------------------

(179) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__ISNATILIST(cons(x0, zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros)) by 
   A__ISNATILIST(cons(0, zeros)) -> c5(A__AND(tt, tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(s(z0), zeros)) -> c5(A__AND(a__isNat(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(length(z0), zeros)) -> c5(A__AND(a__isNatList(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(z0, zeros)) -> c5(A__AND(isNat(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__ISNATILIST(zeros))

----------------------------------------

(180)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, isNatIList(x1)))
   A__ISNATILIST(cons(s(0), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(s(0)))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(nil), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(length(nil)))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__ISNAT(length(z0)))
   A__ISNATILIST(cons(x0, nil)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(nil))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(take(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(0, zeros)) -> c5(A__AND(tt, tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(s(z0), zeros)) -> c5(A__AND(a__isNat(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(length(z0), zeros)) -> c5(A__AND(a__isNatList(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(z0, zeros)) -> c5(A__AND(isNat(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__ISNATILIST(zeros))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, isNatIList(x1)))
   A__ISNATILIST(cons(s(0), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(s(0)))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(nil), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(length(nil)))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__ISNAT(length(z0)))
   A__ISNATILIST(cons(x0, nil)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(nil))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(take(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(0, zeros)) -> c5(A__AND(tt, tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(s(z0), zeros)) -> c5(A__AND(a__isNat(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(length(z0), zeros)) -> c5(A__AND(a__isNatList(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(z0, zeros)) -> c5(A__AND(isNat(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__ISNATILIST(zeros))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__UTAKE2_4, MARK_1, A__TAKE_2, A__ISNATLIST_1, A__LENGTH_1, A__ULENGTH_2

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c26_1, c35_1, c36_1, c37_1, c47_1, c48_1, c19_1, c42_1, c4_1, c5_2, c5_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c15_1, c20_3, c20_2, c21_4, c21_3, c22_4, c22_3, c28_3, c28_2, c29_3, c29_2, c31_2, c29_1, c31_1, c33_2, c33_1, c34_2, c34_1, c38_2, c38_1, c40_2, c40_1, c41_2, c41_1, c43_2, c43_1, c44_2, c44_1, c4_2


----------------------------------------

(181) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing tuple parts
----------------------------------------

(182)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, isNatIList(x1)))
   A__ISNATILIST(cons(s(0), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(s(0)))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(nil), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(length(nil)))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__ISNAT(length(z0)))
   A__ISNATILIST(cons(x0, nil)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(nil))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(take(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(0, zeros)) -> c5(A__AND(tt, tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(s(z0), zeros)) -> c5(A__AND(a__isNat(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(length(z0), zeros)) -> c5(A__AND(a__isNatList(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__ISNATILIST(zeros))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, isNatIList(x1)))
   A__ISNATILIST(cons(s(0), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(s(0)))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(nil), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(length(nil)))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__ISNAT(length(z0)))
   A__ISNATILIST(cons(x0, nil)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(nil))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(take(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(0, zeros)) -> c5(A__AND(tt, tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(s(z0), zeros)) -> c5(A__AND(a__isNat(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(length(z0), zeros)) -> c5(A__AND(a__isNatList(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__ISNATILIST(zeros))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__UTAKE2_4, MARK_1, A__TAKE_2, A__ISNATLIST_1, A__LENGTH_1, A__ULENGTH_2

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c26_1, c35_1, c36_1, c37_1, c47_1, c48_1, c19_1, c42_1, c4_1, c5_2, c5_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c15_1, c20_3, c20_2, c21_4, c21_3, c22_4, c22_3, c28_3, c28_2, c29_3, c29_2, c31_2, c29_1, c31_1, c33_2, c33_1, c34_2, c34_1, c38_2, c38_1, c40_2, c40_1, c41_2, c41_1, c43_2, c43_1, c44_2, c44_1, c4_2


----------------------------------------

(183) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1))) by 
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), A__ISNATILIST(cons(x1, z0)))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNATILIST(cons(x1, zeros)))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNATILIST(cons(x1, cons(z0, z1))))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNATILIST(cons(x1, z0)))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c5(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNATILIST(cons(0, x2)))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(s(z0), x2)))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNATILIST(cons(length(z0), x2)))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c5(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(z0, x2)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c5(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c5(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c5(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c5(A__AND(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__ISNATILIST(cons(x1, x2)))

----------------------------------------

(184)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, isNatIList(x1)))
   A__ISNATILIST(cons(s(0), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(s(0)))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(nil), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(length(nil)))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__ISNAT(length(z0)))
   A__ISNATILIST(cons(x0, nil)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(nil))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(take(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(0, zeros)) -> c5(A__AND(tt, tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(s(z0), zeros)) -> c5(A__AND(a__isNat(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(length(z0), zeros)) -> c5(A__AND(a__isNatList(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNATILIST(cons(x1, zeros)))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNATILIST(cons(x1, cons(z0, z1))))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNATILIST(cons(x1, z0)))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c5(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNATILIST(cons(0, x2)))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(s(z0), x2)))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNATILIST(cons(length(z0), x2)))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c5(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(z0, x2)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c5(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c5(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c5(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c5(A__AND(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__ISNATILIST(cons(x1, x2)))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, isNatIList(x1)))
   A__ISNATILIST(cons(s(0), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(s(0)))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(nil), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(length(nil)))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__ISNAT(length(z0)))
   A__ISNATILIST(cons(x0, nil)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(nil))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(take(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(0, zeros)) -> c5(A__AND(tt, tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(s(z0), zeros)) -> c5(A__AND(a__isNat(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(length(z0), zeros)) -> c5(A__AND(a__isNatList(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNATILIST(cons(x1, zeros)))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNATILIST(cons(x1, cons(z0, z1))))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNATILIST(cons(x1, z0)))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c5(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNATILIST(cons(0, x2)))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(s(z0), x2)))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNATILIST(cons(length(z0), x2)))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c5(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(z0, x2)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c5(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c5(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c5(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c5(A__AND(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__ISNATILIST(cons(x1, x2)))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__UTAKE2_4, MARK_1, A__TAKE_2, A__ISNATLIST_1, A__LENGTH_1, A__ULENGTH_2

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c26_1, c35_1, c36_1, c37_1, c47_1, c48_1, c19_1, c42_1, c4_1, c5_2, c5_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c15_1, c20_3, c20_2, c21_4, c21_3, c22_4, c22_3, c28_3, c28_2, c29_3, c29_2, c31_2, c29_1, c31_1, c33_2, c33_1, c34_2, c34_1, c38_2, c38_1, c40_2, c40_1, c41_2, c41_1, c43_2, c43_1, c44_2, c44_1, c4_2


----------------------------------------

(185) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing tuple parts
----------------------------------------

(186)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, isNatIList(x1)))
   A__ISNATILIST(cons(s(0), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(s(0)))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(nil), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(length(nil)))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__ISNAT(length(z0)))
   A__ISNATILIST(cons(x0, nil)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(nil))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(take(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(0, zeros)) -> c5(A__AND(tt, tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(s(z0), zeros)) -> c5(A__AND(a__isNat(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(length(z0), zeros)) -> c5(A__AND(a__isNatList(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNATILIST(cons(x1, zeros)))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNATILIST(cons(x1, cons(z0, z1))))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNATILIST(cons(x1, z0)))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c5(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNATILIST(cons(0, x2)))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(s(z0), x2)))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNATILIST(cons(length(z0), x2)))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c5(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(z0, x2)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c5(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c5(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c5(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__ISNATILIST(cons(x1, x2)))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, isNatIList(x1)))
   A__ISNATILIST(cons(s(0), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(s(0)))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(nil), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(length(nil)))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__ISNAT(length(z0)))
   A__ISNATILIST(cons(x0, nil)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(nil))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(take(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(0, zeros)) -> c5(A__AND(tt, tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(s(z0), zeros)) -> c5(A__AND(a__isNat(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(length(z0), zeros)) -> c5(A__AND(a__isNatList(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNATILIST(cons(x1, zeros)))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNATILIST(cons(x1, cons(z0, z1))))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNATILIST(cons(x1, z0)))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c5(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNATILIST(cons(0, x2)))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(s(z0), x2)))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNATILIST(cons(length(z0), x2)))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c5(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(z0, x2)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c5(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c5(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c5(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__ISNATILIST(cons(x1, x2)))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__UTAKE2_4, MARK_1, A__TAKE_2, A__ISNATLIST_1, A__LENGTH_1, A__ULENGTH_2

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c26_1, c35_1, c36_1, c37_1, c47_1, c48_1, c19_1, c42_1, c4_1, c5_2, c5_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c15_1, c20_3, c20_2, c21_4, c21_3, c22_4, c22_3, c28_3, c28_2, c29_3, c29_2, c31_2, c29_1, c31_1, c33_2, c33_1, c34_2, c34_1, c38_2, c38_1, c40_2, c40_1, c41_2, c41_1, c43_2, c43_1, c44_2, c44_1, c4_2


----------------------------------------

(187) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0)) by 
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__AND(isNat(z0), isNatIList(x1)), A__ISNATILIST(x1))

----------------------------------------

(188)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, isNatIList(x1)))
   A__ISNATILIST(cons(s(0), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(s(0)))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(nil), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(length(nil)))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__ISNAT(length(z0)))
   A__ISNATILIST(cons(x0, nil)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(nil))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(take(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(0, zeros)) -> c5(A__AND(tt, tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(s(z0), zeros)) -> c5(A__AND(a__isNat(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(length(z0), zeros)) -> c5(A__AND(a__isNatList(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNATILIST(cons(x1, zeros)))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNATILIST(cons(x1, cons(z0, z1))))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNATILIST(cons(x1, z0)))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c5(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNATILIST(cons(0, x2)))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(s(z0), x2)))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNATILIST(cons(length(z0), x2)))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c5(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(z0, x2)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c5(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c5(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c5(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__AND(isNat(z0), isNatIList(x1)), A__ISNATILIST(x1))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, isNatIList(x1)))
   A__ISNATILIST(cons(s(0), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(s(0)))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(nil), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(length(nil)))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__ISNAT(length(z0)))
   A__ISNATILIST(cons(x0, nil)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(nil))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(take(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(0, zeros)) -> c5(A__AND(tt, tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(s(z0), zeros)) -> c5(A__AND(a__isNat(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(length(z0), zeros)) -> c5(A__AND(a__isNatList(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNATILIST(cons(x1, zeros)))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNATILIST(cons(x1, cons(z0, z1))))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNATILIST(cons(x1, z0)))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c5(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNATILIST(cons(0, x2)))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(s(z0), x2)))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNATILIST(cons(length(z0), x2)))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c5(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(z0, x2)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c5(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c5(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c5(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__AND(isNat(z0), isNatIList(x1)), A__ISNATILIST(x1))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__UTAKE2_4, MARK_1, A__TAKE_2, A__ISNATLIST_1, A__LENGTH_1, A__ULENGTH_2

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c26_1, c35_1, c36_1, c37_1, c47_1, c48_1, c19_1, c42_1, c4_1, c5_2, c5_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c15_1, c20_3, c20_2, c21_4, c21_3, c22_4, c22_3, c28_3, c28_2, c29_3, c29_2, c31_2, c29_1, c31_1, c33_2, c33_1, c34_2, c34_1, c38_2, c38_1, c40_2, c40_1, c41_2, c41_1, c43_2, c43_1, c44_2, c44_1, c4_2


----------------------------------------

(189) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing tuple parts
----------------------------------------

(190)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, isNatIList(x1)))
   A__ISNATILIST(cons(s(0), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(s(0)))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(nil), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(length(nil)))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__ISNAT(length(z0)))
   A__ISNATILIST(cons(x0, nil)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(nil))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(take(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(0, zeros)) -> c5(A__AND(tt, tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(s(z0), zeros)) -> c5(A__AND(a__isNat(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(length(z0), zeros)) -> c5(A__AND(a__isNatList(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNATILIST(cons(x1, zeros)))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNATILIST(cons(x1, cons(z0, z1))))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNATILIST(cons(x1, z0)))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c5(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNATILIST(cons(0, x2)))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(s(z0), x2)))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNATILIST(cons(length(z0), x2)))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c5(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(z0, x2)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c5(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c5(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c5(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNATILIST(x1))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, isNatIList(x1)))
   A__ISNATILIST(cons(s(0), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(s(0)))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(nil), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(length(nil)))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__ISNAT(length(z0)))
   A__ISNATILIST(cons(x0, nil)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(nil))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(take(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(0, zeros)) -> c5(A__AND(tt, tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(s(z0), zeros)) -> c5(A__AND(a__isNat(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(length(z0), zeros)) -> c5(A__AND(a__isNatList(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNATILIST(cons(x1, zeros)))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNATILIST(cons(x1, cons(z0, z1))))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNATILIST(cons(x1, z0)))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c5(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNATILIST(cons(0, x2)))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(s(z0), x2)))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNATILIST(cons(length(z0), x2)))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c5(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(z0, x2)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c5(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c5(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c5(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNATILIST(x1))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__UTAKE2_4, MARK_1, A__TAKE_2, A__ISNATLIST_1, A__LENGTH_1, A__ULENGTH_2

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c26_1, c35_1, c36_1, c37_1, c47_1, c48_1, c19_1, c42_1, c4_1, c5_2, c5_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c15_1, c20_3, c20_2, c21_4, c21_3, c22_4, c22_3, c28_3, c28_2, c29_3, c29_2, c31_2, c29_1, c31_1, c33_2, c33_1, c34_2, c34_1, c38_2, c38_1, c40_2, c40_1, c41_2, c41_1, c43_2, c43_1, c44_2, c44_1, c4_2


----------------------------------------

(191) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1)) by 
   A__ISNATILIST(cons(0, z0)) -> c5(A__AND(tt, a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, zeros)) -> c5(A__AND(tt, tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(0, cons(z0, z1))) -> c5(A__AND(tt, a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(0, z0)) -> c5(A__AND(tt, isNatIList(z0)), A__ISNATILIST(z0))

----------------------------------------

(192)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, isNatIList(x1)))
   A__ISNATILIST(cons(s(0), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(s(0)))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(nil), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(length(nil)))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__ISNAT(length(z0)))
   A__ISNATILIST(cons(x0, nil)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(nil))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(take(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(0, zeros)) -> c5(A__AND(tt, tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(s(z0), zeros)) -> c5(A__AND(a__isNat(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(length(z0), zeros)) -> c5(A__AND(a__isNatList(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNATILIST(cons(x1, zeros)))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNATILIST(cons(x1, cons(z0, z1))))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNATILIST(cons(x1, z0)))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c5(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNATILIST(cons(0, x2)))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(s(z0), x2)))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNATILIST(cons(length(z0), x2)))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c5(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(z0, x2)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c5(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c5(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c5(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNATILIST(x1))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, isNatIList(x1)))
   A__ISNATILIST(cons(s(0), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(s(0)))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(nil), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(length(nil)))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__ISNAT(length(z0)))
   A__ISNATILIST(cons(x0, nil)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(nil))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(take(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(0, zeros)) -> c5(A__AND(tt, tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(s(z0), zeros)) -> c5(A__AND(a__isNat(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(length(z0), zeros)) -> c5(A__AND(a__isNatList(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNATILIST(cons(x1, zeros)))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNATILIST(cons(x1, cons(z0, z1))))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNATILIST(cons(x1, z0)))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c5(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNATILIST(cons(0, x2)))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(s(z0), x2)))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNATILIST(cons(length(z0), x2)))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c5(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(z0, x2)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c5(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c5(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c5(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNATILIST(x1))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__UTAKE2_4, MARK_1, A__TAKE_2, A__ISNATLIST_1, A__LENGTH_1, A__ULENGTH_2

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c26_1, c35_1, c36_1, c37_1, c47_1, c48_1, c19_1, c42_1, c4_1, c5_2, c5_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c15_1, c20_3, c20_2, c21_4, c21_3, c22_4, c22_3, c28_3, c28_2, c29_3, c29_2, c31_2, c29_1, c31_1, c33_2, c33_1, c34_2, c34_1, c38_2, c38_1, c40_2, c40_1, c41_2, c41_1, c43_2, c43_1, c44_2, c44_1, c4_2


----------------------------------------

(193) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1)) by 
   A__ISNATILIST(cons(s(x0), z0)) -> c5(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(s(x0), zeros)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(s(x0), cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(s(x0), z0)) -> c5(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(s(0), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))

----------------------------------------

(194)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, isNatIList(x1)))
   A__ISNATILIST(cons(s(0), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(s(0)))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(nil), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(length(nil)))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__ISNAT(length(z0)))
   A__ISNATILIST(cons(x0, nil)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(nil))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(take(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(0, zeros)) -> c5(A__AND(tt, tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(s(z0), zeros)) -> c5(A__AND(a__isNat(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(length(z0), zeros)) -> c5(A__AND(a__isNatList(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNATILIST(cons(x1, zeros)))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNATILIST(cons(x1, cons(z0, z1))))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNATILIST(cons(x1, z0)))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c5(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNATILIST(cons(0, x2)))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(s(z0), x2)))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNATILIST(cons(length(z0), x2)))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c5(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(z0, x2)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c5(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c5(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c5(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(0), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, isNatIList(x1)))
   A__ISNATILIST(cons(s(0), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(s(0)))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(nil), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(length(nil)))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__ISNAT(length(z0)))
   A__ISNATILIST(cons(x0, nil)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(nil))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(take(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(0, zeros)) -> c5(A__AND(tt, tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(s(z0), zeros)) -> c5(A__AND(a__isNat(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(length(z0), zeros)) -> c5(A__AND(a__isNatList(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNATILIST(cons(x1, zeros)))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNATILIST(cons(x1, cons(z0, z1))))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNATILIST(cons(x1, z0)))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c5(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNATILIST(cons(0, x2)))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(s(z0), x2)))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNATILIST(cons(length(z0), x2)))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c5(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(z0, x2)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c5(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c5(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c5(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(0), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__UTAKE2_4, MARK_1, A__TAKE_2, A__ISNATLIST_1, A__LENGTH_1, A__ULENGTH_2

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c26_1, c35_1, c36_1, c37_1, c47_1, c48_1, c19_1, c42_1, c4_1, c5_2, c5_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c15_1, c20_3, c20_2, c21_4, c21_3, c22_4, c22_3, c28_3, c28_2, c29_3, c29_2, c31_2, c29_1, c31_1, c33_2, c33_1, c34_2, c34_1, c38_2, c38_1, c40_2, c40_1, c41_2, c41_1, c43_2, c43_1, c44_2, c44_1, c4_2


----------------------------------------

(195) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing tuple parts
----------------------------------------

(196)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, isNatIList(x1)))
   A__ISNATILIST(cons(s(0), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(s(0)))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(nil), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(length(nil)))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__ISNAT(length(z0)))
   A__ISNATILIST(cons(x0, nil)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(nil))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(take(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(0, zeros)) -> c5(A__AND(tt, tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(s(z0), zeros)) -> c5(A__AND(a__isNat(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(length(z0), zeros)) -> c5(A__AND(a__isNatList(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNATILIST(cons(x1, zeros)))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNATILIST(cons(x1, cons(z0, z1))))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNATILIST(cons(x1, z0)))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c5(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNATILIST(cons(0, x2)))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(s(z0), x2)))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNATILIST(cons(length(z0), x2)))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c5(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(z0, x2)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c5(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c5(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c5(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(0), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__ISNATILIST(x1))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, isNatIList(x1)))
   A__ISNATILIST(cons(s(0), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(s(0)))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(nil), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(length(nil)))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__ISNAT(length(z0)))
   A__ISNATILIST(cons(x0, nil)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(nil))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(take(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(0, zeros)) -> c5(A__AND(tt, tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(s(z0), zeros)) -> c5(A__AND(a__isNat(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(length(z0), zeros)) -> c5(A__AND(a__isNatList(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNATILIST(cons(x1, zeros)))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNATILIST(cons(x1, cons(z0, z1))))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNATILIST(cons(x1, z0)))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c5(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNATILIST(cons(0, x2)))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(s(z0), x2)))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNATILIST(cons(length(z0), x2)))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c5(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(z0, x2)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c5(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c5(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c5(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(0), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__ISNATILIST(x1))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__UTAKE2_4, MARK_1, A__TAKE_2, A__ISNATLIST_1, A__LENGTH_1, A__ULENGTH_2

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c26_1, c35_1, c36_1, c37_1, c47_1, c48_1, c19_1, c42_1, c4_1, c5_2, c5_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c15_1, c20_3, c20_2, c21_4, c21_3, c22_4, c22_3, c28_3, c28_2, c29_3, c29_2, c31_2, c29_1, c31_1, c33_2, c33_1, c34_2, c34_1, c38_2, c38_1, c40_2, c40_1, c41_2, c41_1, c43_2, c43_1, c44_2, c44_1, c4_2


----------------------------------------

(197) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1)) by 
   A__ISNATILIST(cons(length(x0), z0)) -> c5(A__AND(a__isNatList(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(length(x0), zeros)) -> c5(A__AND(a__isNatList(x0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(length(x0), cons(z0, z1))) -> c5(A__AND(a__isNatList(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(length(x0), z0)) -> c5(A__AND(a__isNatList(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(length(nil), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))

----------------------------------------

(198)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, isNatIList(x1)))
   A__ISNATILIST(cons(s(0), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(s(0)))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(nil), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(length(nil)))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__ISNAT(length(z0)))
   A__ISNATILIST(cons(x0, nil)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(nil))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(take(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(0, zeros)) -> c5(A__AND(tt, tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(s(z0), zeros)) -> c5(A__AND(a__isNat(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(length(z0), zeros)) -> c5(A__AND(a__isNatList(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNATILIST(cons(x1, zeros)))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNATILIST(cons(x1, cons(z0, z1))))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNATILIST(cons(x1, z0)))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c5(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNATILIST(cons(0, x2)))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(s(z0), x2)))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNATILIST(cons(length(z0), x2)))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c5(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(z0, x2)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c5(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c5(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c5(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(0), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(nil), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, isNatIList(x1)))
   A__ISNATILIST(cons(s(0), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(s(0)))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(nil), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(length(nil)))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__ISNAT(length(z0)))
   A__ISNATILIST(cons(x0, nil)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(nil))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(take(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(0, zeros)) -> c5(A__AND(tt, tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(s(z0), zeros)) -> c5(A__AND(a__isNat(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(length(z0), zeros)) -> c5(A__AND(a__isNatList(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNATILIST(cons(x1, zeros)))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNATILIST(cons(x1, cons(z0, z1))))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNATILIST(cons(x1, z0)))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c5(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNATILIST(cons(0, x2)))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(s(z0), x2)))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNATILIST(cons(length(z0), x2)))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c5(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(z0, x2)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c5(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c5(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c5(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(0), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(nil), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__UTAKE2_4, MARK_1, A__TAKE_2, A__ISNATLIST_1, A__LENGTH_1, A__ULENGTH_2

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c26_1, c35_1, c36_1, c37_1, c47_1, c48_1, c19_1, c42_1, c4_1, c5_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c15_1, c20_3, c20_2, c21_4, c21_3, c22_4, c22_3, c28_3, c28_2, c29_3, c29_2, c31_2, c29_1, c31_1, c33_2, c33_1, c34_2, c34_1, c38_2, c38_1, c40_2, c40_1, c41_2, c41_1, c43_2, c43_1, c44_2, c44_1, c4_2, c5_2


----------------------------------------

(199) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing tuple parts
----------------------------------------

(200)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, isNatIList(x1)))
   A__ISNATILIST(cons(s(0), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(s(0)))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(nil), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(length(nil)))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__ISNAT(length(z0)))
   A__ISNATILIST(cons(x0, nil)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(nil))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(take(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(0, zeros)) -> c5(A__AND(tt, tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(s(z0), zeros)) -> c5(A__AND(a__isNat(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(length(z0), zeros)) -> c5(A__AND(a__isNatList(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNATILIST(cons(x1, zeros)))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNATILIST(cons(x1, cons(z0, z1))))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNATILIST(cons(x1, z0)))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c5(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNATILIST(cons(0, x2)))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(s(z0), x2)))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNATILIST(cons(length(z0), x2)))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c5(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(z0, x2)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c5(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c5(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c5(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(0), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(nil), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__ISNATILIST(x1))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, isNatIList(x1)))
   A__ISNATILIST(cons(s(0), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(s(0)))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(nil), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(length(nil)))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__ISNAT(length(z0)))
   A__ISNATILIST(cons(x0, nil)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(nil))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(take(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(0, zeros)) -> c5(A__AND(tt, tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(s(z0), zeros)) -> c5(A__AND(a__isNat(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(length(z0), zeros)) -> c5(A__AND(a__isNatList(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNATILIST(cons(x1, zeros)))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNATILIST(cons(x1, cons(z0, z1))))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNATILIST(cons(x1, z0)))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c5(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNATILIST(cons(0, x2)))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(s(z0), x2)))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNATILIST(cons(length(z0), x2)))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c5(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(z0, x2)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c5(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c5(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c5(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(0), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(nil), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__ISNATILIST(x1))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__UTAKE2_4, MARK_1, A__TAKE_2, A__ISNATLIST_1, A__LENGTH_1, A__ULENGTH_2

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c26_1, c35_1, c36_1, c37_1, c47_1, c48_1, c19_1, c42_1, c4_1, c5_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c15_1, c20_3, c20_2, c21_4, c21_3, c22_4, c22_3, c28_3, c28_2, c29_3, c29_2, c31_2, c29_1, c31_1, c33_2, c33_1, c34_2, c34_1, c38_2, c38_1, c40_2, c40_1, c41_2, c41_1, c43_2, c43_1, c44_2, c44_1, c4_2, c5_2


----------------------------------------

(201) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__ISNATLIST(cons(x0, nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(x0)) by 
   A__ISNATLIST(cons(0, nil)) -> c12(A__AND(tt, tt), A__ISNAT(0))
   A__ISNATLIST(cons(s(z0), nil)) -> c12(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), nil)) -> c12(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(z0, nil)) -> c12(A__AND(isNat(z0), tt), A__ISNAT(z0))

----------------------------------------

(202)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, isNatIList(x1)))
   A__ISNATILIST(cons(s(0), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(s(0)))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(nil), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(length(nil)))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__ISNAT(length(z0)))
   A__ISNATILIST(cons(x0, nil)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(nil))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(take(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(0, zeros)) -> c5(A__AND(tt, tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(s(z0), zeros)) -> c5(A__AND(a__isNat(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(length(z0), zeros)) -> c5(A__AND(a__isNatList(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNATILIST(cons(x1, zeros)))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNATILIST(cons(x1, cons(z0, z1))))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNATILIST(cons(x1, z0)))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c5(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNATILIST(cons(0, x2)))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(s(z0), x2)))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNATILIST(cons(length(z0), x2)))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c5(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(z0, x2)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c5(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c5(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c5(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(0), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(nil), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(0, nil)) -> c12(A__AND(tt, tt), A__ISNAT(0))
   A__ISNATLIST(cons(s(z0), nil)) -> c12(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), nil)) -> c12(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(z0, nil)) -> c12(A__AND(isNat(z0), tt), A__ISNAT(z0))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, isNatIList(x1)))
   A__ISNATILIST(cons(s(0), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(s(0)))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(nil), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(length(nil)))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__ISNAT(length(z0)))
   A__ISNATILIST(cons(x0, nil)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(nil))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(take(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(0, zeros)) -> c5(A__AND(tt, tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(s(z0), zeros)) -> c5(A__AND(a__isNat(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(length(z0), zeros)) -> c5(A__AND(a__isNatList(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNATILIST(cons(x1, zeros)))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNATILIST(cons(x1, cons(z0, z1))))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNATILIST(cons(x1, z0)))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c5(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNATILIST(cons(0, x2)))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(s(z0), x2)))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNATILIST(cons(length(z0), x2)))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c5(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(z0, x2)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c5(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c5(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c5(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(0), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(nil), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(0, nil)) -> c12(A__AND(tt, tt), A__ISNAT(0))
   A__ISNATLIST(cons(s(z0), nil)) -> c12(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), nil)) -> c12(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(z0, nil)) -> c12(A__AND(isNat(z0), tt), A__ISNAT(z0))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__UTAKE2_4, MARK_1, A__TAKE_2, A__ISNATLIST_1, A__LENGTH_1, A__ULENGTH_2

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c26_1, c35_1, c36_1, c37_1, c47_1, c48_1, c19_1, c42_1, c4_1, c5_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c15_1, c20_3, c20_2, c21_4, c21_3, c22_4, c22_3, c28_3, c28_2, c29_3, c29_2, c31_2, c29_1, c31_1, c33_2, c33_1, c34_2, c34_1, c38_2, c38_1, c40_2, c40_1, c41_2, c41_1, c43_2, c43_1, c44_2, c44_1, c4_2, c5_2


----------------------------------------

(203) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing tuple parts
----------------------------------------

(204)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, isNatIList(x1)))
   A__ISNATILIST(cons(s(0), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(s(0)))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(nil), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(length(nil)))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__ISNAT(length(z0)))
   A__ISNATILIST(cons(x0, nil)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(nil))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(take(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(0, zeros)) -> c5(A__AND(tt, tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(s(z0), zeros)) -> c5(A__AND(a__isNat(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(length(z0), zeros)) -> c5(A__AND(a__isNatList(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNATILIST(cons(x1, zeros)))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNATILIST(cons(x1, cons(z0, z1))))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNATILIST(cons(x1, z0)))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c5(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNATILIST(cons(0, x2)))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(s(z0), x2)))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNATILIST(cons(length(z0), x2)))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c5(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(z0, x2)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c5(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c5(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c5(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(0), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(nil), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(s(z0), nil)) -> c12(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), nil)) -> c12(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, nil)) -> c12(A__AND(tt, tt))
   A__ISNATLIST(cons(z0, nil)) -> c12(A__ISNAT(z0))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, isNatIList(x1)))
   A__ISNATILIST(cons(s(0), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(s(0)))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(nil), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(length(nil)))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__ISNAT(length(z0)))
   A__ISNATILIST(cons(x0, nil)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(nil))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(take(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(0, zeros)) -> c5(A__AND(tt, tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(s(z0), zeros)) -> c5(A__AND(a__isNat(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(length(z0), zeros)) -> c5(A__AND(a__isNatList(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNATILIST(cons(x1, zeros)))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNATILIST(cons(x1, cons(z0, z1))))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNATILIST(cons(x1, z0)))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c5(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNATILIST(cons(0, x2)))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(s(z0), x2)))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNATILIST(cons(length(z0), x2)))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c5(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(z0, x2)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c5(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c5(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c5(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(0), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(nil), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(s(z0), nil)) -> c12(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), nil)) -> c12(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, nil)) -> c12(A__AND(tt, tt))
   A__ISNATLIST(cons(z0, nil)) -> c12(A__ISNAT(z0))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__UTAKE2_4, MARK_1, A__TAKE_2, A__ISNATLIST_1, A__LENGTH_1, A__ULENGTH_2

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c26_1, c35_1, c36_1, c37_1, c47_1, c48_1, c19_1, c42_1, c4_1, c5_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c15_1, c20_3, c20_2, c21_4, c21_3, c22_4, c22_3, c28_3, c28_2, c29_3, c29_2, c31_2, c29_1, c31_1, c33_2, c33_1, c34_2, c34_1, c38_2, c38_1, c40_2, c40_1, c41_2, c41_1, c43_2, c43_1, c44_2, c44_1, c4_2, c5_2


----------------------------------------

(205) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__ISNATLIST(cons(x0, cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0)) by 
   A__ISNATLIST(cons(x0, cons(x1, x2))) -> c12(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, nil))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, cons(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, take(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(0, x2))) -> c12(A__AND(a__isNat(x0), a__and(tt, a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(s(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(length(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, x2))) -> c12(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(0, cons(x1, x2))) -> c12(A__AND(tt, a__and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(0))
   A__ISNATLIST(cons(s(z0), cons(x1, x2))) -> c12(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), cons(x1, x2))) -> c12(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(z0, cons(x1, x2))) -> c12(A__AND(isNat(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(z0))

----------------------------------------

(206)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, isNatIList(x1)))
   A__ISNATILIST(cons(s(0), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(s(0)))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(nil), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(length(nil)))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__ISNAT(length(z0)))
   A__ISNATILIST(cons(x0, nil)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(nil))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(take(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(0, zeros)) -> c5(A__AND(tt, tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(s(z0), zeros)) -> c5(A__AND(a__isNat(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(length(z0), zeros)) -> c5(A__AND(a__isNatList(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNATILIST(cons(x1, zeros)))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNATILIST(cons(x1, cons(z0, z1))))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNATILIST(cons(x1, z0)))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c5(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNATILIST(cons(0, x2)))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(s(z0), x2)))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNATILIST(cons(length(z0), x2)))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c5(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(z0, x2)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c5(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c5(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c5(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(0), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(nil), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(s(z0), nil)) -> c12(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), nil)) -> c12(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, nil)) -> c12(A__AND(tt, tt))
   A__ISNATLIST(cons(z0, nil)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(x1, x2))) -> c12(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, nil))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, cons(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, take(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(0, x2))) -> c12(A__AND(a__isNat(x0), a__and(tt, a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(s(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(length(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, x2))) -> c12(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(0, cons(x1, x2))) -> c12(A__AND(tt, a__and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(0))
   A__ISNATLIST(cons(s(z0), cons(x1, x2))) -> c12(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), cons(x1, x2))) -> c12(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(z0, cons(x1, x2))) -> c12(A__AND(isNat(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(z0))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, isNatIList(x1)))
   A__ISNATILIST(cons(s(0), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(s(0)))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(nil), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(length(nil)))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__ISNAT(length(z0)))
   A__ISNATILIST(cons(x0, nil)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(nil))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(take(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(0, zeros)) -> c5(A__AND(tt, tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(s(z0), zeros)) -> c5(A__AND(a__isNat(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(length(z0), zeros)) -> c5(A__AND(a__isNatList(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNATILIST(cons(x1, zeros)))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNATILIST(cons(x1, cons(z0, z1))))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNATILIST(cons(x1, z0)))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c5(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNATILIST(cons(0, x2)))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(s(z0), x2)))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNATILIST(cons(length(z0), x2)))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c5(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(z0, x2)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c5(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c5(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c5(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(0), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(nil), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(s(z0), nil)) -> c12(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), nil)) -> c12(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, nil)) -> c12(A__AND(tt, tt))
   A__ISNATLIST(cons(z0, nil)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(x1, x2))) -> c12(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, nil))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, cons(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, take(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(0, x2))) -> c12(A__AND(a__isNat(x0), a__and(tt, a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(s(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(length(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, x2))) -> c12(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(0, cons(x1, x2))) -> c12(A__AND(tt, a__and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(0))
   A__ISNATLIST(cons(s(z0), cons(x1, x2))) -> c12(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), cons(x1, x2))) -> c12(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(z0, cons(x1, x2))) -> c12(A__AND(isNat(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(z0))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__UTAKE2_4, MARK_1, A__TAKE_2, A__ISNATLIST_1, A__LENGTH_1, A__ULENGTH_2

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c26_1, c35_1, c36_1, c37_1, c47_1, c48_1, c19_1, c42_1, c4_1, c5_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c15_1, c20_3, c20_2, c21_4, c21_3, c22_4, c22_3, c28_3, c28_2, c29_3, c29_2, c31_2, c29_1, c31_1, c33_2, c33_1, c34_2, c34_1, c38_2, c38_1, c40_2, c40_1, c41_2, c41_1, c43_2, c43_1, c44_2, c44_1, c4_2, c5_2


----------------------------------------

(207) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing tuple parts
----------------------------------------

(208)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, isNatIList(x1)))
   A__ISNATILIST(cons(s(0), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(s(0)))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(nil), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(length(nil)))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__ISNAT(length(z0)))
   A__ISNATILIST(cons(x0, nil)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(nil))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(take(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(0, zeros)) -> c5(A__AND(tt, tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(s(z0), zeros)) -> c5(A__AND(a__isNat(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(length(z0), zeros)) -> c5(A__AND(a__isNatList(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNATILIST(cons(x1, zeros)))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNATILIST(cons(x1, cons(z0, z1))))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNATILIST(cons(x1, z0)))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c5(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNATILIST(cons(0, x2)))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(s(z0), x2)))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNATILIST(cons(length(z0), x2)))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c5(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(z0, x2)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c5(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c5(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c5(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(0), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(nil), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(s(z0), nil)) -> c12(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), nil)) -> c12(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, nil)) -> c12(A__AND(tt, tt))
   A__ISNATLIST(cons(z0, nil)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(x1, x2))) -> c12(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, nil))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, cons(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, take(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(0, x2))) -> c12(A__AND(a__isNat(x0), a__and(tt, a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(s(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(length(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, x2))) -> c12(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), cons(x1, x2))) -> c12(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), cons(x1, x2))) -> c12(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, cons(x1, x2))) -> c12(A__AND(tt, a__and(a__isNat(x1), a__isNatList(x2))))
   A__ISNATLIST(cons(z0, cons(x1, x2))) -> c12(A__ISNAT(z0))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, isNatIList(x1)))
   A__ISNATILIST(cons(s(0), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(s(0)))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(nil), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(length(nil)))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__ISNAT(length(z0)))
   A__ISNATILIST(cons(x0, nil)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(nil))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(take(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(0, zeros)) -> c5(A__AND(tt, tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(s(z0), zeros)) -> c5(A__AND(a__isNat(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(length(z0), zeros)) -> c5(A__AND(a__isNatList(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNATILIST(cons(x1, zeros)))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNATILIST(cons(x1, cons(z0, z1))))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNATILIST(cons(x1, z0)))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c5(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNATILIST(cons(0, x2)))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(s(z0), x2)))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNATILIST(cons(length(z0), x2)))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c5(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(z0, x2)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c5(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c5(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c5(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(0), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(nil), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(s(z0), nil)) -> c12(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), nil)) -> c12(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, nil)) -> c12(A__AND(tt, tt))
   A__ISNATLIST(cons(z0, nil)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(x1, x2))) -> c12(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, nil))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, cons(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, take(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(0, x2))) -> c12(A__AND(a__isNat(x0), a__and(tt, a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(s(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(length(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, x2))) -> c12(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), cons(x1, x2))) -> c12(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), cons(x1, x2))) -> c12(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, cons(x1, x2))) -> c12(A__AND(tt, a__and(a__isNat(x1), a__isNatList(x2))))
   A__ISNATLIST(cons(z0, cons(x1, x2))) -> c12(A__ISNAT(z0))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__UTAKE2_4, MARK_1, A__TAKE_2, A__ISNATLIST_1, A__LENGTH_1, A__ULENGTH_2

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c26_1, c35_1, c36_1, c37_1, c47_1, c48_1, c19_1, c42_1, c4_1, c5_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c15_1, c20_3, c20_2, c21_4, c21_3, c22_4, c22_3, c28_3, c28_2, c29_3, c29_2, c31_2, c29_1, c31_1, c33_2, c33_1, c34_2, c34_1, c38_2, c38_1, c40_2, c40_1, c41_2, c41_1, c43_2, c43_1, c44_2, c44_1, c4_2, c5_2


----------------------------------------

(209) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__ISNATLIST(cons(x0, take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0)) by 
   A__ISNATLIST(cons(x0, take(x1, x2))) -> c12(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, zeros))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, cons(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(0, x2))) -> c12(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(s(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(length(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, x2))) -> c12(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(0, take(x1, x2))) -> c12(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(0))
   A__ISNATLIST(cons(s(z0), take(x1, x2))) -> c12(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), take(x1, x2))) -> c12(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(z0, take(x1, x2))) -> c12(A__AND(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))

----------------------------------------

(210)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, isNatIList(x1)))
   A__ISNATILIST(cons(s(0), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(s(0)))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(nil), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(length(nil)))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__ISNAT(length(z0)))
   A__ISNATILIST(cons(x0, nil)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(nil))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(take(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(0, zeros)) -> c5(A__AND(tt, tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(s(z0), zeros)) -> c5(A__AND(a__isNat(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(length(z0), zeros)) -> c5(A__AND(a__isNatList(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNATILIST(cons(x1, zeros)))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNATILIST(cons(x1, cons(z0, z1))))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNATILIST(cons(x1, z0)))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c5(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNATILIST(cons(0, x2)))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(s(z0), x2)))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNATILIST(cons(length(z0), x2)))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c5(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(z0, x2)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c5(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c5(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c5(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(0), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(nil), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(s(z0), nil)) -> c12(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), nil)) -> c12(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, nil)) -> c12(A__AND(tt, tt))
   A__ISNATLIST(cons(z0, nil)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(x1, x2))) -> c12(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, nil))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, cons(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, take(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(0, x2))) -> c12(A__AND(a__isNat(x0), a__and(tt, a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(s(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(length(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, x2))) -> c12(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), cons(x1, x2))) -> c12(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), cons(x1, x2))) -> c12(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, cons(x1, x2))) -> c12(A__AND(tt, a__and(a__isNat(x1), a__isNatList(x2))))
   A__ISNATLIST(cons(z0, cons(x1, x2))) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, take(x1, x2))) -> c12(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, zeros))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, cons(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(0, x2))) -> c12(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(s(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(length(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, x2))) -> c12(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(0, take(x1, x2))) -> c12(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(0))
   A__ISNATLIST(cons(s(z0), take(x1, x2))) -> c12(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), take(x1, x2))) -> c12(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(z0, take(x1, x2))) -> c12(A__AND(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, isNatIList(x1)))
   A__ISNATILIST(cons(s(0), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(s(0)))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(nil), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(length(nil)))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__ISNAT(length(z0)))
   A__ISNATILIST(cons(x0, nil)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(nil))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(take(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(0, zeros)) -> c5(A__AND(tt, tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(s(z0), zeros)) -> c5(A__AND(a__isNat(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(length(z0), zeros)) -> c5(A__AND(a__isNatList(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNATILIST(cons(x1, zeros)))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNATILIST(cons(x1, cons(z0, z1))))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNATILIST(cons(x1, z0)))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c5(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNATILIST(cons(0, x2)))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(s(z0), x2)))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNATILIST(cons(length(z0), x2)))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c5(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(z0, x2)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c5(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c5(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c5(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(0), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(nil), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(s(z0), nil)) -> c12(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), nil)) -> c12(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, nil)) -> c12(A__AND(tt, tt))
   A__ISNATLIST(cons(z0, nil)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(x1, x2))) -> c12(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, nil))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, cons(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, take(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(0, x2))) -> c12(A__AND(a__isNat(x0), a__and(tt, a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(s(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(length(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, x2))) -> c12(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), cons(x1, x2))) -> c12(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), cons(x1, x2))) -> c12(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, cons(x1, x2))) -> c12(A__AND(tt, a__and(a__isNat(x1), a__isNatList(x2))))
   A__ISNATLIST(cons(z0, cons(x1, x2))) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, take(x1, x2))) -> c12(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, zeros))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, cons(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(0, x2))) -> c12(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(s(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(length(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, x2))) -> c12(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(0, take(x1, x2))) -> c12(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(0))
   A__ISNATLIST(cons(s(z0), take(x1, x2))) -> c12(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), take(x1, x2))) -> c12(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(z0, take(x1, x2))) -> c12(A__AND(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__UTAKE2_4, MARK_1, A__TAKE_2, A__ISNATLIST_1, A__LENGTH_1, A__ULENGTH_2

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c26_1, c35_1, c36_1, c37_1, c47_1, c48_1, c19_1, c42_1, c4_1, c5_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c15_1, c20_3, c20_2, c21_4, c21_3, c22_4, c22_3, c28_3, c28_2, c29_3, c29_2, c31_2, c29_1, c31_1, c33_2, c33_1, c34_2, c34_1, c38_2, c38_1, c40_2, c40_1, c41_2, c41_1, c43_2, c43_1, c44_2, c44_1, c4_2, c5_2


----------------------------------------

(211) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing tuple parts
----------------------------------------

(212)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, isNatIList(x1)))
   A__ISNATILIST(cons(s(0), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(s(0)))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(nil), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(length(nil)))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__ISNAT(length(z0)))
   A__ISNATILIST(cons(x0, nil)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(nil))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(take(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(0, zeros)) -> c5(A__AND(tt, tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(s(z0), zeros)) -> c5(A__AND(a__isNat(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(length(z0), zeros)) -> c5(A__AND(a__isNatList(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNATILIST(cons(x1, zeros)))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNATILIST(cons(x1, cons(z0, z1))))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNATILIST(cons(x1, z0)))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c5(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNATILIST(cons(0, x2)))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(s(z0), x2)))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNATILIST(cons(length(z0), x2)))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c5(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(z0, x2)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c5(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c5(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c5(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(0), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(nil), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(s(z0), nil)) -> c12(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), nil)) -> c12(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, nil)) -> c12(A__AND(tt, tt))
   A__ISNATLIST(cons(z0, nil)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(x1, x2))) -> c12(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, nil))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, cons(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, take(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(0, x2))) -> c12(A__AND(a__isNat(x0), a__and(tt, a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(s(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(length(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, x2))) -> c12(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), cons(x1, x2))) -> c12(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), cons(x1, x2))) -> c12(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, cons(x1, x2))) -> c12(A__AND(tt, a__and(a__isNat(x1), a__isNatList(x2))))
   A__ISNATLIST(cons(z0, cons(x1, x2))) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, take(x1, x2))) -> c12(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, zeros))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, cons(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(0, x2))) -> c12(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(s(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(length(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, x2))) -> c12(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), take(x1, x2))) -> c12(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), take(x1, x2))) -> c12(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, take(x1, x2))) -> c12(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATLIST(cons(z0, take(x1, x2))) -> c12(A__ISNAT(z0))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, isNatIList(x1)))
   A__ISNATILIST(cons(s(0), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(s(0)))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(nil), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(length(nil)))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__ISNAT(length(z0)))
   A__ISNATILIST(cons(x0, nil)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(nil))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(take(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(0, zeros)) -> c5(A__AND(tt, tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(s(z0), zeros)) -> c5(A__AND(a__isNat(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(length(z0), zeros)) -> c5(A__AND(a__isNatList(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNATILIST(cons(x1, zeros)))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNATILIST(cons(x1, cons(z0, z1))))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNATILIST(cons(x1, z0)))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c5(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNATILIST(cons(0, x2)))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(s(z0), x2)))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNATILIST(cons(length(z0), x2)))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c5(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(z0, x2)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c5(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c5(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c5(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(0), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(nil), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(s(z0), nil)) -> c12(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), nil)) -> c12(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, nil)) -> c12(A__AND(tt, tt))
   A__ISNATLIST(cons(z0, nil)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(x1, x2))) -> c12(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, nil))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, cons(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, take(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(0, x2))) -> c12(A__AND(a__isNat(x0), a__and(tt, a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(s(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(length(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, x2))) -> c12(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), cons(x1, x2))) -> c12(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), cons(x1, x2))) -> c12(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, cons(x1, x2))) -> c12(A__AND(tt, a__and(a__isNat(x1), a__isNatList(x2))))
   A__ISNATLIST(cons(z0, cons(x1, x2))) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, take(x1, x2))) -> c12(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, zeros))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, cons(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(0, x2))) -> c12(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(s(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(length(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, x2))) -> c12(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), take(x1, x2))) -> c12(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), take(x1, x2))) -> c12(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, take(x1, x2))) -> c12(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATLIST(cons(z0, take(x1, x2))) -> c12(A__ISNAT(z0))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__UTAKE2_4, MARK_1, A__TAKE_2, A__ISNATLIST_1, A__LENGTH_1, A__ULENGTH_2

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c26_1, c35_1, c36_1, c37_1, c47_1, c48_1, c19_1, c42_1, c4_1, c5_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c15_1, c20_3, c20_2, c21_4, c21_3, c22_4, c22_3, c28_3, c28_2, c29_3, c29_2, c31_2, c29_1, c31_1, c33_2, c33_1, c34_2, c34_1, c38_2, c38_1, c40_2, c40_1, c41_2, c41_1, c43_2, c43_1, c44_2, c44_1, c4_2, c5_2


----------------------------------------

(213) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__ISNATLIST(cons(x0, z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0)) by 
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, isNatList(x1)), A__ISNAT(0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__AND(isNat(z0), isNatList(x1)), A__ISNAT(z0))

----------------------------------------

(214)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, isNatIList(x1)))
   A__ISNATILIST(cons(s(0), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(s(0)))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(nil), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(length(nil)))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__ISNAT(length(z0)))
   A__ISNATILIST(cons(x0, nil)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(nil))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(take(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(0, zeros)) -> c5(A__AND(tt, tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(s(z0), zeros)) -> c5(A__AND(a__isNat(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(length(z0), zeros)) -> c5(A__AND(a__isNatList(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNATILIST(cons(x1, zeros)))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNATILIST(cons(x1, cons(z0, z1))))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNATILIST(cons(x1, z0)))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c5(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNATILIST(cons(0, x2)))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(s(z0), x2)))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNATILIST(cons(length(z0), x2)))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c5(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(z0, x2)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c5(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c5(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c5(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(0), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(nil), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(s(z0), nil)) -> c12(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), nil)) -> c12(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, nil)) -> c12(A__AND(tt, tt))
   A__ISNATLIST(cons(z0, nil)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(x1, x2))) -> c12(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, nil))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, cons(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, take(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(0, x2))) -> c12(A__AND(a__isNat(x0), a__and(tt, a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(s(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(length(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, x2))) -> c12(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), cons(x1, x2))) -> c12(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), cons(x1, x2))) -> c12(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, cons(x1, x2))) -> c12(A__AND(tt, a__and(a__isNat(x1), a__isNatList(x2))))
   A__ISNATLIST(cons(z0, cons(x1, x2))) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, take(x1, x2))) -> c12(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, zeros))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, cons(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(0, x2))) -> c12(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(s(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(length(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, x2))) -> c12(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), take(x1, x2))) -> c12(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), take(x1, x2))) -> c12(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, take(x1, x2))) -> c12(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATLIST(cons(z0, take(x1, x2))) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, isNatList(x1)), A__ISNAT(0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__AND(isNat(z0), isNatList(x1)), A__ISNAT(z0))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, isNatIList(x1)))
   A__ISNATILIST(cons(s(0), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(s(0)))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(nil), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(length(nil)))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__ISNAT(length(z0)))
   A__ISNATILIST(cons(x0, nil)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(nil))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(take(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(0, zeros)) -> c5(A__AND(tt, tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(s(z0), zeros)) -> c5(A__AND(a__isNat(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(length(z0), zeros)) -> c5(A__AND(a__isNatList(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNATILIST(cons(x1, zeros)))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNATILIST(cons(x1, cons(z0, z1))))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNATILIST(cons(x1, z0)))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c5(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNATILIST(cons(0, x2)))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(s(z0), x2)))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNATILIST(cons(length(z0), x2)))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c5(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(z0, x2)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c5(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c5(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c5(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(0), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(nil), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(s(z0), nil)) -> c12(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), nil)) -> c12(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, nil)) -> c12(A__AND(tt, tt))
   A__ISNATLIST(cons(z0, nil)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(x1, x2))) -> c12(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, nil))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, cons(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, take(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(0, x2))) -> c12(A__AND(a__isNat(x0), a__and(tt, a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(s(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(length(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, x2))) -> c12(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), cons(x1, x2))) -> c12(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), cons(x1, x2))) -> c12(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, cons(x1, x2))) -> c12(A__AND(tt, a__and(a__isNat(x1), a__isNatList(x2))))
   A__ISNATLIST(cons(z0, cons(x1, x2))) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, take(x1, x2))) -> c12(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, zeros))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, cons(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(0, x2))) -> c12(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(s(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(length(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, x2))) -> c12(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), take(x1, x2))) -> c12(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), take(x1, x2))) -> c12(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, take(x1, x2))) -> c12(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATLIST(cons(z0, take(x1, x2))) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, isNatList(x1)), A__ISNAT(0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__AND(isNat(z0), isNatList(x1)), A__ISNAT(z0))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__UTAKE2_4, MARK_1, A__TAKE_2, A__ISNATLIST_1, A__LENGTH_1, A__ULENGTH_2

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c26_1, c35_1, c36_1, c37_1, c47_1, c48_1, c19_1, c42_1, c4_1, c5_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c15_1, c20_3, c20_2, c21_4, c21_3, c22_4, c22_3, c28_3, c28_2, c29_3, c29_2, c31_2, c29_1, c31_1, c33_2, c33_1, c34_2, c34_1, c38_2, c38_1, c40_2, c40_1, c41_2, c41_1, c43_2, c43_1, c44_2, c44_1, c4_2, c5_2


----------------------------------------

(215) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing tuple parts
----------------------------------------

(216)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, isNatIList(x1)))
   A__ISNATILIST(cons(s(0), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(s(0)))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(nil), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(length(nil)))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__ISNAT(length(z0)))
   A__ISNATILIST(cons(x0, nil)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(nil))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(take(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(0, zeros)) -> c5(A__AND(tt, tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(s(z0), zeros)) -> c5(A__AND(a__isNat(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(length(z0), zeros)) -> c5(A__AND(a__isNatList(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNATILIST(cons(x1, zeros)))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNATILIST(cons(x1, cons(z0, z1))))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNATILIST(cons(x1, z0)))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c5(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNATILIST(cons(0, x2)))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(s(z0), x2)))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNATILIST(cons(length(z0), x2)))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c5(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(z0, x2)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c5(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c5(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c5(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(0), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(nil), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(s(z0), nil)) -> c12(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), nil)) -> c12(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, nil)) -> c12(A__AND(tt, tt))
   A__ISNATLIST(cons(z0, nil)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(x1, x2))) -> c12(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, nil))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, cons(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, take(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(0, x2))) -> c12(A__AND(a__isNat(x0), a__and(tt, a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(s(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(length(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, x2))) -> c12(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), cons(x1, x2))) -> c12(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), cons(x1, x2))) -> c12(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, cons(x1, x2))) -> c12(A__AND(tt, a__and(a__isNat(x1), a__isNatList(x2))))
   A__ISNATLIST(cons(z0, cons(x1, x2))) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, take(x1, x2))) -> c12(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, zeros))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, cons(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(0, x2))) -> c12(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(s(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(length(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, x2))) -> c12(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), take(x1, x2))) -> c12(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), take(x1, x2))) -> c12(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, take(x1, x2))) -> c12(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATLIST(cons(z0, take(x1, x2))) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, isNatList(x1)))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, isNatIList(x1)))
   A__ISNATILIST(cons(s(0), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(s(0)))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(nil), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(length(nil)))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__ISNAT(length(z0)))
   A__ISNATILIST(cons(x0, nil)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(nil))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(take(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(0, zeros)) -> c5(A__AND(tt, tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(s(z0), zeros)) -> c5(A__AND(a__isNat(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(length(z0), zeros)) -> c5(A__AND(a__isNatList(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNATILIST(cons(x1, zeros)))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNATILIST(cons(x1, cons(z0, z1))))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNATILIST(cons(x1, z0)))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c5(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNATILIST(cons(0, x2)))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(s(z0), x2)))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNATILIST(cons(length(z0), x2)))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c5(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(z0, x2)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c5(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c5(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c5(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(0), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(nil), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(s(z0), nil)) -> c12(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), nil)) -> c12(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, nil)) -> c12(A__AND(tt, tt))
   A__ISNATLIST(cons(z0, nil)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(x1, x2))) -> c12(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, nil))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, cons(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, take(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(0, x2))) -> c12(A__AND(a__isNat(x0), a__and(tt, a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(s(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(length(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, x2))) -> c12(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), cons(x1, x2))) -> c12(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), cons(x1, x2))) -> c12(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, cons(x1, x2))) -> c12(A__AND(tt, a__and(a__isNat(x1), a__isNatList(x2))))
   A__ISNATLIST(cons(z0, cons(x1, x2))) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, take(x1, x2))) -> c12(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, zeros))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, cons(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(0, x2))) -> c12(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(s(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(length(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, x2))) -> c12(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), take(x1, x2))) -> c12(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), take(x1, x2))) -> c12(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, take(x1, x2))) -> c12(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATLIST(cons(z0, take(x1, x2))) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, isNatList(x1)))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__UTAKE2_4, MARK_1, A__TAKE_2, A__ISNATLIST_1, A__LENGTH_1, A__ULENGTH_2

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c26_1, c35_1, c36_1, c37_1, c47_1, c48_1, c19_1, c42_1, c4_1, c5_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c15_1, c20_3, c20_2, c21_4, c21_3, c22_4, c22_3, c28_3, c28_2, c29_3, c29_2, c31_2, c29_1, c31_1, c33_2, c33_1, c34_2, c34_1, c38_2, c38_1, c40_2, c40_1, c41_2, c41_1, c43_2, c43_1, c44_2, c44_1, c4_2, c5_2


----------------------------------------

(217) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0))) by 
   A__ISNATLIST(cons(s(x0), nil)) -> c12(A__AND(a__isNat(x0), tt), A__ISNAT(s(x0)))
   A__ISNATLIST(cons(s(x0), cons(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(s(x0)))
   A__ISNATLIST(cons(s(x0), take(z0, z1))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(s(x0)))
   A__ISNATLIST(cons(s(x0), z0)) -> c12(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(s(x0)))
   A__ISNATLIST(cons(s(0), x1)) -> c12(A__AND(tt, a__isNatList(x1)), A__ISNAT(s(0)))
   A__ISNATLIST(cons(s(s(z0)), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATLIST(cons(s(length(z0)), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))

----------------------------------------

(218)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, isNatIList(x1)))
   A__ISNATILIST(cons(s(0), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(s(0)))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(nil), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(length(nil)))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__ISNAT(length(z0)))
   A__ISNATILIST(cons(x0, nil)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(nil))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(take(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(0, zeros)) -> c5(A__AND(tt, tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(s(z0), zeros)) -> c5(A__AND(a__isNat(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(length(z0), zeros)) -> c5(A__AND(a__isNatList(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNATILIST(cons(x1, zeros)))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNATILIST(cons(x1, cons(z0, z1))))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNATILIST(cons(x1, z0)))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c5(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNATILIST(cons(0, x2)))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(s(z0), x2)))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNATILIST(cons(length(z0), x2)))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c5(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(z0, x2)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c5(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c5(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c5(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(0), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(nil), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(s(z0), nil)) -> c12(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), nil)) -> c12(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, nil)) -> c12(A__AND(tt, tt))
   A__ISNATLIST(cons(z0, nil)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(x1, x2))) -> c12(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, nil))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, cons(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, take(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(0, x2))) -> c12(A__AND(a__isNat(x0), a__and(tt, a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(s(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(length(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, x2))) -> c12(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), cons(x1, x2))) -> c12(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), cons(x1, x2))) -> c12(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, cons(x1, x2))) -> c12(A__AND(tt, a__and(a__isNat(x1), a__isNatList(x2))))
   A__ISNATLIST(cons(z0, cons(x1, x2))) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, take(x1, x2))) -> c12(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, zeros))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, cons(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(0, x2))) -> c12(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(s(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(length(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, x2))) -> c12(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), take(x1, x2))) -> c12(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), take(x1, x2))) -> c12(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, take(x1, x2))) -> c12(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATLIST(cons(z0, take(x1, x2))) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, isNatList(x1)))
   A__ISNATLIST(cons(s(0), x1)) -> c12(A__AND(tt, a__isNatList(x1)), A__ISNAT(s(0)))
   A__ISNATLIST(cons(s(s(z0)), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATLIST(cons(s(length(z0)), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, isNatIList(x1)))
   A__ISNATILIST(cons(s(0), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(s(0)))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(nil), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(length(nil)))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__ISNAT(length(z0)))
   A__ISNATILIST(cons(x0, nil)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(nil))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(take(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(0, zeros)) -> c5(A__AND(tt, tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(s(z0), zeros)) -> c5(A__AND(a__isNat(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(length(z0), zeros)) -> c5(A__AND(a__isNatList(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNATILIST(cons(x1, zeros)))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNATILIST(cons(x1, cons(z0, z1))))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNATILIST(cons(x1, z0)))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c5(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNATILIST(cons(0, x2)))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(s(z0), x2)))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNATILIST(cons(length(z0), x2)))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c5(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(z0, x2)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c5(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c5(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c5(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(0), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(nil), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(s(z0), nil)) -> c12(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), nil)) -> c12(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, nil)) -> c12(A__AND(tt, tt))
   A__ISNATLIST(cons(z0, nil)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(x1, x2))) -> c12(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, nil))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, cons(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, take(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(0, x2))) -> c12(A__AND(a__isNat(x0), a__and(tt, a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(s(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(length(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, x2))) -> c12(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), cons(x1, x2))) -> c12(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), cons(x1, x2))) -> c12(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, cons(x1, x2))) -> c12(A__AND(tt, a__and(a__isNat(x1), a__isNatList(x2))))
   A__ISNATLIST(cons(z0, cons(x1, x2))) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, take(x1, x2))) -> c12(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, zeros))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, cons(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(0, x2))) -> c12(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(s(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(length(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, x2))) -> c12(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), take(x1, x2))) -> c12(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), take(x1, x2))) -> c12(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, take(x1, x2))) -> c12(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATLIST(cons(z0, take(x1, x2))) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, isNatList(x1)))
   A__ISNATLIST(cons(s(0), x1)) -> c12(A__AND(tt, a__isNatList(x1)), A__ISNAT(s(0)))
   A__ISNATLIST(cons(s(s(z0)), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATLIST(cons(s(length(z0)), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__UTAKE2_4, MARK_1, A__TAKE_2, A__ISNATLIST_1, A__LENGTH_1, A__ULENGTH_2

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c26_1, c35_1, c36_1, c37_1, c47_1, c48_1, c19_1, c42_1, c4_1, c5_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c15_1, c20_3, c20_2, c21_4, c21_3, c22_4, c22_3, c28_3, c28_2, c29_3, c29_2, c31_2, c29_1, c31_1, c33_2, c33_1, c34_2, c34_1, c38_2, c38_1, c40_2, c40_1, c41_2, c41_1, c43_2, c43_1, c44_2, c44_1, c4_2, c5_2


----------------------------------------

(219) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing tuple parts
----------------------------------------

(220)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, isNatIList(x1)))
   A__ISNATILIST(cons(s(0), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(s(0)))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(nil), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(length(nil)))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__ISNAT(length(z0)))
   A__ISNATILIST(cons(x0, nil)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(nil))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(take(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(0, zeros)) -> c5(A__AND(tt, tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(s(z0), zeros)) -> c5(A__AND(a__isNat(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(length(z0), zeros)) -> c5(A__AND(a__isNatList(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNATILIST(cons(x1, zeros)))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNATILIST(cons(x1, cons(z0, z1))))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNATILIST(cons(x1, z0)))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c5(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNATILIST(cons(0, x2)))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(s(z0), x2)))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNATILIST(cons(length(z0), x2)))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c5(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(z0, x2)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c5(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c5(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c5(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(0), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(nil), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(s(z0), nil)) -> c12(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), nil)) -> c12(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, nil)) -> c12(A__AND(tt, tt))
   A__ISNATLIST(cons(z0, nil)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(x1, x2))) -> c12(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, nil))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, cons(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, take(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(0, x2))) -> c12(A__AND(a__isNat(x0), a__and(tt, a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(s(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(length(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, x2))) -> c12(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), cons(x1, x2))) -> c12(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), cons(x1, x2))) -> c12(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, cons(x1, x2))) -> c12(A__AND(tt, a__and(a__isNat(x1), a__isNatList(x2))))
   A__ISNATLIST(cons(z0, cons(x1, x2))) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, take(x1, x2))) -> c12(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, zeros))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, cons(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(0, x2))) -> c12(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(s(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(length(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, x2))) -> c12(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), take(x1, x2))) -> c12(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), take(x1, x2))) -> c12(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, take(x1, x2))) -> c12(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATLIST(cons(z0, take(x1, x2))) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, isNatList(x1)))
   A__ISNATLIST(cons(s(0), x1)) -> c12(A__AND(tt, a__isNatList(x1)), A__ISNAT(s(0)))
   A__ISNATLIST(cons(s(s(z0)), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATLIST(cons(s(length(z0)), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__ISNAT(s(z0)))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, isNatIList(x1)))
   A__ISNATILIST(cons(s(0), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(s(0)))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(nil), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(length(nil)))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__ISNAT(length(z0)))
   A__ISNATILIST(cons(x0, nil)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(nil))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(take(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(0, zeros)) -> c5(A__AND(tt, tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(s(z0), zeros)) -> c5(A__AND(a__isNat(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(length(z0), zeros)) -> c5(A__AND(a__isNatList(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNATILIST(cons(x1, zeros)))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNATILIST(cons(x1, cons(z0, z1))))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNATILIST(cons(x1, z0)))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c5(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNATILIST(cons(0, x2)))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(s(z0), x2)))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNATILIST(cons(length(z0), x2)))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c5(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(z0, x2)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c5(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c5(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c5(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(0), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(nil), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(s(z0), nil)) -> c12(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), nil)) -> c12(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, nil)) -> c12(A__AND(tt, tt))
   A__ISNATLIST(cons(z0, nil)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(x1, x2))) -> c12(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, nil))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, cons(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, take(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(0, x2))) -> c12(A__AND(a__isNat(x0), a__and(tt, a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(s(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(length(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, x2))) -> c12(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), cons(x1, x2))) -> c12(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), cons(x1, x2))) -> c12(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, cons(x1, x2))) -> c12(A__AND(tt, a__and(a__isNat(x1), a__isNatList(x2))))
   A__ISNATLIST(cons(z0, cons(x1, x2))) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, take(x1, x2))) -> c12(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, zeros))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, cons(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(0, x2))) -> c12(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(s(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(length(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, x2))) -> c12(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), take(x1, x2))) -> c12(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), take(x1, x2))) -> c12(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, take(x1, x2))) -> c12(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATLIST(cons(z0, take(x1, x2))) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, isNatList(x1)))
   A__ISNATLIST(cons(s(0), x1)) -> c12(A__AND(tt, a__isNatList(x1)), A__ISNAT(s(0)))
   A__ISNATLIST(cons(s(s(z0)), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATLIST(cons(s(length(z0)), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__ISNAT(s(z0)))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__UTAKE2_4, MARK_1, A__TAKE_2, A__ISNATLIST_1, A__LENGTH_1, A__ULENGTH_2

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c26_1, c35_1, c36_1, c37_1, c47_1, c48_1, c19_1, c42_1, c4_1, c5_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c15_1, c20_3, c20_2, c21_4, c21_3, c22_4, c22_3, c28_3, c28_2, c29_3, c29_2, c31_2, c29_1, c31_1, c33_2, c33_1, c34_2, c34_1, c38_2, c38_1, c40_2, c40_1, c41_2, c41_1, c43_2, c43_1, c44_2, c44_1, c4_2, c5_2


----------------------------------------

(221) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0))) by 
   A__ISNATLIST(cons(length(x0), nil)) -> c12(A__AND(a__isNatList(x0), tt), A__ISNAT(length(x0)))
   A__ISNATLIST(cons(length(x0), cons(z0, z1))) -> c12(A__AND(a__isNatList(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(length(x0)))
   A__ISNATLIST(cons(length(x0), take(z0, z1))) -> c12(A__AND(a__isNatList(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(length(x0)))
   A__ISNATLIST(cons(length(x0), z0)) -> c12(A__AND(a__isNatList(x0), isNatList(z0)), A__ISNAT(length(x0)))
   A__ISNATLIST(cons(length(nil), x1)) -> c12(A__AND(tt, a__isNatList(x1)), A__ISNAT(length(nil)))
   A__ISNATLIST(cons(length(cons(z0, z1)), x1)) -> c12(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATLIST(cons(length(take(z0, z1)), x1)) -> c12(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))

----------------------------------------

(222)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, isNatIList(x1)))
   A__ISNATILIST(cons(s(0), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(s(0)))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(nil), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(length(nil)))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__ISNAT(length(z0)))
   A__ISNATILIST(cons(x0, nil)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(nil))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(take(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(0, zeros)) -> c5(A__AND(tt, tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(s(z0), zeros)) -> c5(A__AND(a__isNat(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(length(z0), zeros)) -> c5(A__AND(a__isNatList(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNATILIST(cons(x1, zeros)))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNATILIST(cons(x1, cons(z0, z1))))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNATILIST(cons(x1, z0)))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c5(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNATILIST(cons(0, x2)))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(s(z0), x2)))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNATILIST(cons(length(z0), x2)))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c5(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(z0, x2)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c5(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c5(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c5(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(0), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(nil), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(s(z0), nil)) -> c12(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), nil)) -> c12(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, nil)) -> c12(A__AND(tt, tt))
   A__ISNATLIST(cons(z0, nil)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(x1, x2))) -> c12(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, nil))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, cons(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, take(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(0, x2))) -> c12(A__AND(a__isNat(x0), a__and(tt, a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(s(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(length(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, x2))) -> c12(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), cons(x1, x2))) -> c12(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), cons(x1, x2))) -> c12(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, cons(x1, x2))) -> c12(A__AND(tt, a__and(a__isNat(x1), a__isNatList(x2))))
   A__ISNATLIST(cons(z0, cons(x1, x2))) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, take(x1, x2))) -> c12(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, zeros))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, cons(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(0, x2))) -> c12(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(s(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(length(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, x2))) -> c12(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), take(x1, x2))) -> c12(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), take(x1, x2))) -> c12(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, take(x1, x2))) -> c12(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATLIST(cons(z0, take(x1, x2))) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, isNatList(x1)))
   A__ISNATLIST(cons(s(0), x1)) -> c12(A__AND(tt, a__isNatList(x1)), A__ISNAT(s(0)))
   A__ISNATLIST(cons(s(s(z0)), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATLIST(cons(s(length(z0)), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(nil), x1)) -> c12(A__AND(tt, a__isNatList(x1)), A__ISNAT(length(nil)))
   A__ISNATLIST(cons(length(cons(z0, z1)), x1)) -> c12(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATLIST(cons(length(take(z0, z1)), x1)) -> c12(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, isNatIList(x1)))
   A__ISNATILIST(cons(s(0), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(s(0)))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(nil), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(length(nil)))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__ISNAT(length(z0)))
   A__ISNATILIST(cons(x0, nil)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(nil))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(take(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(0, zeros)) -> c5(A__AND(tt, tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(s(z0), zeros)) -> c5(A__AND(a__isNat(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(length(z0), zeros)) -> c5(A__AND(a__isNatList(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNATILIST(cons(x1, zeros)))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNATILIST(cons(x1, cons(z0, z1))))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNATILIST(cons(x1, z0)))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c5(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNATILIST(cons(0, x2)))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(s(z0), x2)))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNATILIST(cons(length(z0), x2)))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c5(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(z0, x2)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c5(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c5(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c5(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(0), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(nil), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(s(z0), nil)) -> c12(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), nil)) -> c12(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, nil)) -> c12(A__AND(tt, tt))
   A__ISNATLIST(cons(z0, nil)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(x1, x2))) -> c12(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, nil))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, cons(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, take(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(0, x2))) -> c12(A__AND(a__isNat(x0), a__and(tt, a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(s(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(length(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, x2))) -> c12(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), cons(x1, x2))) -> c12(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), cons(x1, x2))) -> c12(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, cons(x1, x2))) -> c12(A__AND(tt, a__and(a__isNat(x1), a__isNatList(x2))))
   A__ISNATLIST(cons(z0, cons(x1, x2))) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, take(x1, x2))) -> c12(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, zeros))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, cons(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(0, x2))) -> c12(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(s(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(length(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, x2))) -> c12(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), take(x1, x2))) -> c12(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), take(x1, x2))) -> c12(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, take(x1, x2))) -> c12(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATLIST(cons(z0, take(x1, x2))) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, isNatList(x1)))
   A__ISNATLIST(cons(s(0), x1)) -> c12(A__AND(tt, a__isNatList(x1)), A__ISNAT(s(0)))
   A__ISNATLIST(cons(s(s(z0)), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATLIST(cons(s(length(z0)), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(nil), x1)) -> c12(A__AND(tt, a__isNatList(x1)), A__ISNAT(length(nil)))
   A__ISNATLIST(cons(length(cons(z0, z1)), x1)) -> c12(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATLIST(cons(length(take(z0, z1)), x1)) -> c12(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__UTAKE2_4, MARK_1, A__TAKE_2, A__ISNATLIST_1, A__LENGTH_1, A__ULENGTH_2

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c26_1, c35_1, c36_1, c37_1, c47_1, c48_1, c19_1, c42_1, c4_1, c5_1, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c15_1, c20_3, c20_2, c21_4, c21_3, c22_4, c22_3, c28_3, c28_2, c29_3, c29_2, c31_2, c29_1, c31_1, c33_2, c33_1, c34_2, c34_1, c38_2, c38_1, c40_2, c40_1, c41_2, c41_1, c43_2, c43_1, c44_2, c44_1, c4_2, c5_2, c12_2


----------------------------------------

(223) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing tuple parts
----------------------------------------

(224)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, isNatIList(x1)))
   A__ISNATILIST(cons(s(0), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(s(0)))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(nil), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(length(nil)))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__ISNAT(length(z0)))
   A__ISNATILIST(cons(x0, nil)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(nil))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(take(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(0, zeros)) -> c5(A__AND(tt, tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(s(z0), zeros)) -> c5(A__AND(a__isNat(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(length(z0), zeros)) -> c5(A__AND(a__isNatList(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNATILIST(cons(x1, zeros)))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNATILIST(cons(x1, cons(z0, z1))))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNATILIST(cons(x1, z0)))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c5(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNATILIST(cons(0, x2)))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(s(z0), x2)))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNATILIST(cons(length(z0), x2)))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c5(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(z0, x2)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c5(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c5(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c5(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(0), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(nil), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(s(z0), nil)) -> c12(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), nil)) -> c12(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, nil)) -> c12(A__AND(tt, tt))
   A__ISNATLIST(cons(z0, nil)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(x1, x2))) -> c12(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, nil))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, cons(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, take(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(0, x2))) -> c12(A__AND(a__isNat(x0), a__and(tt, a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(s(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(length(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, x2))) -> c12(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), cons(x1, x2))) -> c12(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), cons(x1, x2))) -> c12(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, cons(x1, x2))) -> c12(A__AND(tt, a__and(a__isNat(x1), a__isNatList(x2))))
   A__ISNATLIST(cons(z0, cons(x1, x2))) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, take(x1, x2))) -> c12(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, zeros))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, cons(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(0, x2))) -> c12(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(s(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(length(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, x2))) -> c12(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), take(x1, x2))) -> c12(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), take(x1, x2))) -> c12(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, take(x1, x2))) -> c12(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATLIST(cons(z0, take(x1, x2))) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, isNatList(x1)))
   A__ISNATLIST(cons(s(0), x1)) -> c12(A__AND(tt, a__isNatList(x1)), A__ISNAT(s(0)))
   A__ISNATLIST(cons(s(s(z0)), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATLIST(cons(s(length(z0)), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(nil), x1)) -> c12(A__AND(tt, a__isNatList(x1)), A__ISNAT(length(nil)))
   A__ISNATLIST(cons(length(cons(z0, z1)), x1)) -> c12(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATLIST(cons(length(take(z0, z1)), x1)) -> c12(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__ISNAT(length(z0)))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1)))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, isNatIList(x1)))
   A__ISNATILIST(cons(s(0), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(s(0)))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(nil), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(length(nil)))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__ISNAT(length(z0)))
   A__ISNATILIST(cons(x0, nil)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(nil))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(take(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(0, zeros)) -> c5(A__AND(tt, tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(s(z0), zeros)) -> c5(A__AND(a__isNat(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(length(z0), zeros)) -> c5(A__AND(a__isNatList(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNATILIST(cons(x1, zeros)))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNATILIST(cons(x1, cons(z0, z1))))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNATILIST(cons(x1, z0)))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c5(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNATILIST(cons(0, x2)))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(s(z0), x2)))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNATILIST(cons(length(z0), x2)))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c5(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(z0, x2)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c5(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c5(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c5(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(0), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(nil), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(s(z0), nil)) -> c12(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), nil)) -> c12(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, nil)) -> c12(A__AND(tt, tt))
   A__ISNATLIST(cons(z0, nil)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(x1, x2))) -> c12(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, nil))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, cons(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, take(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(0, x2))) -> c12(A__AND(a__isNat(x0), a__and(tt, a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(s(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(length(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, x2))) -> c12(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), cons(x1, x2))) -> c12(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), cons(x1, x2))) -> c12(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, cons(x1, x2))) -> c12(A__AND(tt, a__and(a__isNat(x1), a__isNatList(x2))))
   A__ISNATLIST(cons(z0, cons(x1, x2))) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, take(x1, x2))) -> c12(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, zeros))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, cons(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(0, x2))) -> c12(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(s(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(length(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, x2))) -> c12(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), take(x1, x2))) -> c12(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), take(x1, x2))) -> c12(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, take(x1, x2))) -> c12(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATLIST(cons(z0, take(x1, x2))) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, isNatList(x1)))
   A__ISNATLIST(cons(s(0), x1)) -> c12(A__AND(tt, a__isNatList(x1)), A__ISNAT(s(0)))
   A__ISNATLIST(cons(s(s(z0)), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATLIST(cons(s(length(z0)), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(nil), x1)) -> c12(A__AND(tt, a__isNatList(x1)), A__ISNAT(length(nil)))
   A__ISNATLIST(cons(length(cons(z0, z1)), x1)) -> c12(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATLIST(cons(length(take(z0, z1)), x1)) -> c12(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__ISNAT(length(z0)))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__UTAKE2_4, MARK_1, A__TAKE_2, A__ISNATLIST_1, A__LENGTH_1, A__ULENGTH_2

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c26_1, c35_1, c36_1, c37_1, c47_1, c48_1, c19_1, c42_1, c4_1, c5_1, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c15_1, c20_3, c20_2, c21_4, c21_3, c22_4, c22_3, c28_3, c28_2, c29_3, c29_2, c31_2, c29_1, c31_1, c33_2, c33_1, c34_2, c34_1, c38_2, c38_1, c40_2, c40_1, c41_2, c41_1, c43_2, c43_1, c44_2, c44_1, c4_2, c5_2, c12_2


----------------------------------------

(225) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, a__isNatList(x1))) by 
   A__ISNATLIST(cons(0, nil)) -> c12(A__AND(tt, tt))
   A__ISNATLIST(cons(0, cons(z0, z1))) -> c12(A__AND(tt, a__and(a__isNat(z0), a__isNatList(z1))))
   A__ISNATLIST(cons(0, take(z0, z1))) -> c12(A__AND(tt, a__and(a__isNat(z0), a__isNatIList(z1))))
   A__ISNATLIST(cons(0, z0)) -> c12(A__AND(tt, isNatList(z0)))

----------------------------------------

(226)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, isNatIList(x1)))
   A__ISNATILIST(cons(s(0), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(s(0)))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(nil), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(length(nil)))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__ISNAT(length(z0)))
   A__ISNATILIST(cons(x0, nil)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(nil))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(take(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(0, zeros)) -> c5(A__AND(tt, tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(s(z0), zeros)) -> c5(A__AND(a__isNat(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(length(z0), zeros)) -> c5(A__AND(a__isNatList(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNATILIST(cons(x1, zeros)))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNATILIST(cons(x1, cons(z0, z1))))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNATILIST(cons(x1, z0)))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c5(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNATILIST(cons(0, x2)))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(s(z0), x2)))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNATILIST(cons(length(z0), x2)))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c5(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(z0, x2)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c5(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c5(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c5(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(0), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(nil), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(s(z0), nil)) -> c12(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), nil)) -> c12(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, nil)) -> c12(A__AND(tt, tt))
   A__ISNATLIST(cons(z0, nil)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(x1, x2))) -> c12(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, nil))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, cons(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, take(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(0, x2))) -> c12(A__AND(a__isNat(x0), a__and(tt, a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(s(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(length(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, x2))) -> c12(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), cons(x1, x2))) -> c12(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), cons(x1, x2))) -> c12(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, cons(x1, x2))) -> c12(A__AND(tt, a__and(a__isNat(x1), a__isNatList(x2))))
   A__ISNATLIST(cons(z0, cons(x1, x2))) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, take(x1, x2))) -> c12(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, zeros))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, cons(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(0, x2))) -> c12(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(s(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(length(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, x2))) -> c12(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), take(x1, x2))) -> c12(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), take(x1, x2))) -> c12(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, take(x1, x2))) -> c12(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATLIST(cons(z0, take(x1, x2))) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, isNatList(x1)))
   A__ISNATLIST(cons(s(0), x1)) -> c12(A__AND(tt, a__isNatList(x1)), A__ISNAT(s(0)))
   A__ISNATLIST(cons(s(s(z0)), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATLIST(cons(s(length(z0)), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(nil), x1)) -> c12(A__AND(tt, a__isNatList(x1)), A__ISNAT(length(nil)))
   A__ISNATLIST(cons(length(cons(z0, z1)), x1)) -> c12(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATLIST(cons(length(take(z0, z1)), x1)) -> c12(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__ISNAT(length(z0)))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1)))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, isNatIList(x1)))
   A__ISNATILIST(cons(s(0), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(s(0)))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(nil), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(length(nil)))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__ISNAT(length(z0)))
   A__ISNATILIST(cons(x0, nil)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(nil))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(take(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(0, zeros)) -> c5(A__AND(tt, tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(s(z0), zeros)) -> c5(A__AND(a__isNat(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(length(z0), zeros)) -> c5(A__AND(a__isNatList(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNATILIST(cons(x1, zeros)))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNATILIST(cons(x1, cons(z0, z1))))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNATILIST(cons(x1, z0)))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c5(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNATILIST(cons(0, x2)))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(s(z0), x2)))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNATILIST(cons(length(z0), x2)))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c5(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(z0, x2)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c5(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c5(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c5(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(0), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(nil), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(s(z0), nil)) -> c12(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), nil)) -> c12(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, nil)) -> c12(A__AND(tt, tt))
   A__ISNATLIST(cons(z0, nil)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(x1, x2))) -> c12(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, nil))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, cons(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, take(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(0, x2))) -> c12(A__AND(a__isNat(x0), a__and(tt, a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(s(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(length(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, x2))) -> c12(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), cons(x1, x2))) -> c12(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), cons(x1, x2))) -> c12(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, cons(x1, x2))) -> c12(A__AND(tt, a__and(a__isNat(x1), a__isNatList(x2))))
   A__ISNATLIST(cons(z0, cons(x1, x2))) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, take(x1, x2))) -> c12(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, zeros))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, cons(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(0, x2))) -> c12(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(s(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(length(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, x2))) -> c12(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), take(x1, x2))) -> c12(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), take(x1, x2))) -> c12(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, take(x1, x2))) -> c12(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATLIST(cons(z0, take(x1, x2))) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, isNatList(x1)))
   A__ISNATLIST(cons(s(0), x1)) -> c12(A__AND(tt, a__isNatList(x1)), A__ISNAT(s(0)))
   A__ISNATLIST(cons(s(s(z0)), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATLIST(cons(s(length(z0)), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(nil), x1)) -> c12(A__AND(tt, a__isNatList(x1)), A__ISNAT(length(nil)))
   A__ISNATLIST(cons(length(cons(z0, z1)), x1)) -> c12(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATLIST(cons(length(take(z0, z1)), x1)) -> c12(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__ISNAT(length(z0)))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__UTAKE2_4, MARK_1, A__TAKE_2, A__ISNATLIST_1, A__LENGTH_1, A__ULENGTH_2

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c26_1, c35_1, c36_1, c37_1, c47_1, c48_1, c19_1, c42_1, c4_1, c5_1, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c15_1, c20_3, c20_2, c21_4, c21_3, c22_4, c22_3, c28_3, c28_2, c29_3, c29_2, c31_2, c29_1, c31_1, c33_2, c33_1, c34_2, c34_1, c38_2, c38_1, c40_2, c40_1, c41_2, c41_1, c43_2, c43_1, c44_2, c44_1, c4_2, c5_2, c12_2


----------------------------------------

(227) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__ISNATLIST(cons(x0, cons(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATLIST(cons(z0, z1))) by 
   A__ISNATLIST(cons(x0, cons(x1, x2))) -> c13(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatList(x2))), A__ISNATLIST(cons(x1, x2)))
   A__ISNATLIST(cons(x0, cons(x1, nil))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNATLIST(cons(x1, nil)))
   A__ISNATLIST(cons(x0, cons(x1, cons(z0, z1)))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatList(z1)))), A__ISNATLIST(cons(x1, cons(z0, z1))))
   A__ISNATLIST(cons(x0, cons(x1, take(z0, z1)))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNATLIST(cons(x1, take(z0, z1))))
   A__ISNATLIST(cons(x0, cons(x1, z0))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatList(z0))), A__ISNATLIST(cons(x1, z0)))
   A__ISNATLIST(cons(x0, cons(0, x2))) -> c13(A__AND(a__isNat(x0), a__and(tt, a__isNatList(x2))), A__ISNATLIST(cons(0, x2)))
   A__ISNATLIST(cons(x0, cons(s(z0), x2))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(x2))), A__ISNATLIST(cons(s(z0), x2)))
   A__ISNATLIST(cons(x0, cons(length(z0), x2))) -> c13(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatList(x2))), A__ISNATLIST(cons(length(z0), x2)))
   A__ISNATLIST(cons(x0, cons(z0, x2))) -> c13(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatList(x2))), A__ISNATLIST(cons(z0, x2)))
   A__ISNATLIST(cons(0, cons(x1, x2))) -> c13(A__AND(tt, a__and(a__isNat(x1), a__isNatList(x2))), A__ISNATLIST(cons(x1, x2)))
   A__ISNATLIST(cons(s(z0), cons(x1, x2))) -> c13(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNATLIST(cons(x1, x2)))
   A__ISNATLIST(cons(length(z0), cons(x1, x2))) -> c13(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNATLIST(cons(x1, x2)))
   A__ISNATLIST(cons(z0, cons(x1, x2))) -> c13(A__AND(isNat(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNATLIST(cons(x1, x2)))

----------------------------------------

(228)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, isNatIList(x1)))
   A__ISNATILIST(cons(s(0), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(s(0)))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(nil), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(length(nil)))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__ISNAT(length(z0)))
   A__ISNATILIST(cons(x0, nil)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(nil))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(take(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(0, zeros)) -> c5(A__AND(tt, tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(s(z0), zeros)) -> c5(A__AND(a__isNat(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(length(z0), zeros)) -> c5(A__AND(a__isNatList(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNATILIST(cons(x1, zeros)))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNATILIST(cons(x1, cons(z0, z1))))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNATILIST(cons(x1, z0)))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c5(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNATILIST(cons(0, x2)))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(s(z0), x2)))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNATILIST(cons(length(z0), x2)))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c5(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(z0, x2)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c5(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c5(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c5(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(0), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(nil), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(s(z0), nil)) -> c12(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), nil)) -> c12(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, nil)) -> c12(A__AND(tt, tt))
   A__ISNATLIST(cons(z0, nil)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(x1, x2))) -> c12(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, nil))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, cons(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, take(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(0, x2))) -> c12(A__AND(a__isNat(x0), a__and(tt, a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(s(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(length(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, x2))) -> c12(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), cons(x1, x2))) -> c12(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), cons(x1, x2))) -> c12(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, cons(x1, x2))) -> c12(A__AND(tt, a__and(a__isNat(x1), a__isNatList(x2))))
   A__ISNATLIST(cons(z0, cons(x1, x2))) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, take(x1, x2))) -> c12(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, zeros))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, cons(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(0, x2))) -> c12(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(s(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(length(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, x2))) -> c12(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), take(x1, x2))) -> c12(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), take(x1, x2))) -> c12(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, take(x1, x2))) -> c12(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATLIST(cons(z0, take(x1, x2))) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, isNatList(x1)))
   A__ISNATLIST(cons(s(0), x1)) -> c12(A__AND(tt, a__isNatList(x1)), A__ISNAT(s(0)))
   A__ISNATLIST(cons(s(s(z0)), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATLIST(cons(s(length(z0)), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(nil), x1)) -> c12(A__AND(tt, a__isNatList(x1)), A__ISNAT(length(nil)))
   A__ISNATLIST(cons(length(cons(z0, z1)), x1)) -> c12(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATLIST(cons(length(take(z0, z1)), x1)) -> c12(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__ISNAT(length(z0)))
   A__ISNATLIST(cons(x0, cons(x1, x2))) -> c13(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatList(x2))), A__ISNATLIST(cons(x1, x2)))
   A__ISNATLIST(cons(x0, cons(x1, nil))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNATLIST(cons(x1, nil)))
   A__ISNATLIST(cons(x0, cons(x1, cons(z0, z1)))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatList(z1)))), A__ISNATLIST(cons(x1, cons(z0, z1))))
   A__ISNATLIST(cons(x0, cons(x1, take(z0, z1)))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNATLIST(cons(x1, take(z0, z1))))
   A__ISNATLIST(cons(x0, cons(x1, z0))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatList(z0))), A__ISNATLIST(cons(x1, z0)))
   A__ISNATLIST(cons(x0, cons(0, x2))) -> c13(A__AND(a__isNat(x0), a__and(tt, a__isNatList(x2))), A__ISNATLIST(cons(0, x2)))
   A__ISNATLIST(cons(x0, cons(s(z0), x2))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(x2))), A__ISNATLIST(cons(s(z0), x2)))
   A__ISNATLIST(cons(x0, cons(length(z0), x2))) -> c13(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatList(x2))), A__ISNATLIST(cons(length(z0), x2)))
   A__ISNATLIST(cons(x0, cons(z0, x2))) -> c13(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatList(x2))), A__ISNATLIST(cons(z0, x2)))
   A__ISNATLIST(cons(0, cons(x1, x2))) -> c13(A__AND(tt, a__and(a__isNat(x1), a__isNatList(x2))), A__ISNATLIST(cons(x1, x2)))
   A__ISNATLIST(cons(s(z0), cons(x1, x2))) -> c13(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNATLIST(cons(x1, x2)))
   A__ISNATLIST(cons(length(z0), cons(x1, x2))) -> c13(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNATLIST(cons(x1, x2)))
   A__ISNATLIST(cons(z0, cons(x1, x2))) -> c13(A__AND(isNat(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNATLIST(cons(x1, x2)))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, isNatIList(x1)))
   A__ISNATILIST(cons(s(0), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(s(0)))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(nil), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(length(nil)))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__ISNAT(length(z0)))
   A__ISNATILIST(cons(x0, nil)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(nil))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(take(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(0, zeros)) -> c5(A__AND(tt, tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(s(z0), zeros)) -> c5(A__AND(a__isNat(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(length(z0), zeros)) -> c5(A__AND(a__isNatList(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNATILIST(cons(x1, zeros)))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNATILIST(cons(x1, cons(z0, z1))))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNATILIST(cons(x1, z0)))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c5(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNATILIST(cons(0, x2)))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(s(z0), x2)))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNATILIST(cons(length(z0), x2)))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c5(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(z0, x2)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c5(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c5(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c5(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(0), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(nil), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(s(z0), nil)) -> c12(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), nil)) -> c12(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, nil)) -> c12(A__AND(tt, tt))
   A__ISNATLIST(cons(z0, nil)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(x1, x2))) -> c12(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, nil))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, cons(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, take(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(0, x2))) -> c12(A__AND(a__isNat(x0), a__and(tt, a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(s(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(length(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, x2))) -> c12(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), cons(x1, x2))) -> c12(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), cons(x1, x2))) -> c12(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, cons(x1, x2))) -> c12(A__AND(tt, a__and(a__isNat(x1), a__isNatList(x2))))
   A__ISNATLIST(cons(z0, cons(x1, x2))) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, take(x1, x2))) -> c12(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, zeros))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, cons(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(0, x2))) -> c12(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(s(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(length(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, x2))) -> c12(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), take(x1, x2))) -> c12(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), take(x1, x2))) -> c12(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, take(x1, x2))) -> c12(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATLIST(cons(z0, take(x1, x2))) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, isNatList(x1)))
   A__ISNATLIST(cons(s(0), x1)) -> c12(A__AND(tt, a__isNatList(x1)), A__ISNAT(s(0)))
   A__ISNATLIST(cons(s(s(z0)), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATLIST(cons(s(length(z0)), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(nil), x1)) -> c12(A__AND(tt, a__isNatList(x1)), A__ISNAT(length(nil)))
   A__ISNATLIST(cons(length(cons(z0, z1)), x1)) -> c12(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATLIST(cons(length(take(z0, z1)), x1)) -> c12(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__ISNAT(length(z0)))
   A__ISNATLIST(cons(x0, cons(x1, x2))) -> c13(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatList(x2))), A__ISNATLIST(cons(x1, x2)))
   A__ISNATLIST(cons(x0, cons(x1, nil))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNATLIST(cons(x1, nil)))
   A__ISNATLIST(cons(x0, cons(x1, cons(z0, z1)))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatList(z1)))), A__ISNATLIST(cons(x1, cons(z0, z1))))
   A__ISNATLIST(cons(x0, cons(x1, take(z0, z1)))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNATLIST(cons(x1, take(z0, z1))))
   A__ISNATLIST(cons(x0, cons(x1, z0))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatList(z0))), A__ISNATLIST(cons(x1, z0)))
   A__ISNATLIST(cons(x0, cons(0, x2))) -> c13(A__AND(a__isNat(x0), a__and(tt, a__isNatList(x2))), A__ISNATLIST(cons(0, x2)))
   A__ISNATLIST(cons(x0, cons(s(z0), x2))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(x2))), A__ISNATLIST(cons(s(z0), x2)))
   A__ISNATLIST(cons(x0, cons(length(z0), x2))) -> c13(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatList(x2))), A__ISNATLIST(cons(length(z0), x2)))
   A__ISNATLIST(cons(x0, cons(z0, x2))) -> c13(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatList(x2))), A__ISNATLIST(cons(z0, x2)))
   A__ISNATLIST(cons(0, cons(x1, x2))) -> c13(A__AND(tt, a__and(a__isNat(x1), a__isNatList(x2))), A__ISNATLIST(cons(x1, x2)))
   A__ISNATLIST(cons(s(z0), cons(x1, x2))) -> c13(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNATLIST(cons(x1, x2)))
   A__ISNATLIST(cons(length(z0), cons(x1, x2))) -> c13(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNATLIST(cons(x1, x2)))
   A__ISNATLIST(cons(z0, cons(x1, x2))) -> c13(A__AND(isNat(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNATLIST(cons(x1, x2)))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__UTAKE2_4, MARK_1, A__TAKE_2, A__ISNATLIST_1, A__LENGTH_1, A__ULENGTH_2

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c26_1, c35_1, c36_1, c37_1, c47_1, c48_1, c19_1, c42_1, c4_1, c5_1, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c15_1, c20_3, c20_2, c21_4, c21_3, c22_4, c22_3, c28_3, c28_2, c29_3, c29_2, c31_2, c29_1, c31_1, c33_2, c33_1, c34_2, c34_1, c38_2, c38_1, c40_2, c40_1, c41_2, c41_1, c43_2, c43_1, c44_2, c44_1, c4_2, c5_2, c12_2


----------------------------------------

(229) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing tuple parts
----------------------------------------

(230)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, isNatIList(x1)))
   A__ISNATILIST(cons(s(0), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(s(0)))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(nil), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(length(nil)))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__ISNAT(length(z0)))
   A__ISNATILIST(cons(x0, nil)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(nil))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(take(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(0, zeros)) -> c5(A__AND(tt, tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(s(z0), zeros)) -> c5(A__AND(a__isNat(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(length(z0), zeros)) -> c5(A__AND(a__isNatList(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNATILIST(cons(x1, zeros)))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNATILIST(cons(x1, cons(z0, z1))))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNATILIST(cons(x1, z0)))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c5(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNATILIST(cons(0, x2)))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(s(z0), x2)))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNATILIST(cons(length(z0), x2)))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c5(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(z0, x2)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c5(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c5(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c5(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(0), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(nil), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(s(z0), nil)) -> c12(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), nil)) -> c12(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, nil)) -> c12(A__AND(tt, tt))
   A__ISNATLIST(cons(z0, nil)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(x1, x2))) -> c12(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, nil))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, cons(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, take(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(0, x2))) -> c12(A__AND(a__isNat(x0), a__and(tt, a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(s(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(length(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, x2))) -> c12(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), cons(x1, x2))) -> c12(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), cons(x1, x2))) -> c12(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, cons(x1, x2))) -> c12(A__AND(tt, a__and(a__isNat(x1), a__isNatList(x2))))
   A__ISNATLIST(cons(z0, cons(x1, x2))) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, take(x1, x2))) -> c12(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, zeros))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, cons(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(0, x2))) -> c12(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(s(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(length(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, x2))) -> c12(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), take(x1, x2))) -> c12(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), take(x1, x2))) -> c12(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, take(x1, x2))) -> c12(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATLIST(cons(z0, take(x1, x2))) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, isNatList(x1)))
   A__ISNATLIST(cons(s(0), x1)) -> c12(A__AND(tt, a__isNatList(x1)), A__ISNAT(s(0)))
   A__ISNATLIST(cons(s(s(z0)), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATLIST(cons(s(length(z0)), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(nil), x1)) -> c12(A__AND(tt, a__isNatList(x1)), A__ISNAT(length(nil)))
   A__ISNATLIST(cons(length(cons(z0, z1)), x1)) -> c12(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATLIST(cons(length(take(z0, z1)), x1)) -> c12(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__ISNAT(length(z0)))
   A__ISNATLIST(cons(x0, cons(x1, x2))) -> c13(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatList(x2))), A__ISNATLIST(cons(x1, x2)))
   A__ISNATLIST(cons(x0, cons(x1, nil))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNATLIST(cons(x1, nil)))
   A__ISNATLIST(cons(x0, cons(x1, cons(z0, z1)))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatList(z1)))), A__ISNATLIST(cons(x1, cons(z0, z1))))
   A__ISNATLIST(cons(x0, cons(x1, take(z0, z1)))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNATLIST(cons(x1, take(z0, z1))))
   A__ISNATLIST(cons(x0, cons(x1, z0))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatList(z0))), A__ISNATLIST(cons(x1, z0)))
   A__ISNATLIST(cons(x0, cons(0, x2))) -> c13(A__AND(a__isNat(x0), a__and(tt, a__isNatList(x2))), A__ISNATLIST(cons(0, x2)))
   A__ISNATLIST(cons(x0, cons(s(z0), x2))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(x2))), A__ISNATLIST(cons(s(z0), x2)))
   A__ISNATLIST(cons(x0, cons(length(z0), x2))) -> c13(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatList(x2))), A__ISNATLIST(cons(length(z0), x2)))
   A__ISNATLIST(cons(x0, cons(z0, x2))) -> c13(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatList(x2))), A__ISNATLIST(cons(z0, x2)))
   A__ISNATLIST(cons(0, cons(x1, x2))) -> c13(A__AND(tt, a__and(a__isNat(x1), a__isNatList(x2))), A__ISNATLIST(cons(x1, x2)))
   A__ISNATLIST(cons(s(z0), cons(x1, x2))) -> c13(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNATLIST(cons(x1, x2)))
   A__ISNATLIST(cons(length(z0), cons(x1, x2))) -> c13(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNATLIST(cons(x1, x2)))
   A__ISNATLIST(cons(z0, cons(x1, x2))) -> c13(A__ISNATLIST(cons(x1, x2)))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1)))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, isNatIList(x1)))
   A__ISNATILIST(cons(s(0), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(s(0)))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(nil), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(length(nil)))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__ISNAT(length(z0)))
   A__ISNATILIST(cons(x0, nil)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(nil))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(take(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(0, zeros)) -> c5(A__AND(tt, tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(s(z0), zeros)) -> c5(A__AND(a__isNat(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(length(z0), zeros)) -> c5(A__AND(a__isNatList(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNATILIST(cons(x1, zeros)))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNATILIST(cons(x1, cons(z0, z1))))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNATILIST(cons(x1, z0)))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c5(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNATILIST(cons(0, x2)))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(s(z0), x2)))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNATILIST(cons(length(z0), x2)))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c5(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(z0, x2)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c5(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c5(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c5(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(0), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(nil), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(s(z0), nil)) -> c12(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), nil)) -> c12(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, nil)) -> c12(A__AND(tt, tt))
   A__ISNATLIST(cons(z0, nil)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(x1, x2))) -> c12(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, nil))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, cons(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, take(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(0, x2))) -> c12(A__AND(a__isNat(x0), a__and(tt, a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(s(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(length(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, x2))) -> c12(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), cons(x1, x2))) -> c12(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), cons(x1, x2))) -> c12(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, cons(x1, x2))) -> c12(A__AND(tt, a__and(a__isNat(x1), a__isNatList(x2))))
   A__ISNATLIST(cons(z0, cons(x1, x2))) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, take(x1, x2))) -> c12(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, zeros))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, cons(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(0, x2))) -> c12(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(s(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(length(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, x2))) -> c12(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), take(x1, x2))) -> c12(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), take(x1, x2))) -> c12(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, take(x1, x2))) -> c12(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATLIST(cons(z0, take(x1, x2))) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, isNatList(x1)))
   A__ISNATLIST(cons(s(0), x1)) -> c12(A__AND(tt, a__isNatList(x1)), A__ISNAT(s(0)))
   A__ISNATLIST(cons(s(s(z0)), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATLIST(cons(s(length(z0)), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(nil), x1)) -> c12(A__AND(tt, a__isNatList(x1)), A__ISNAT(length(nil)))
   A__ISNATLIST(cons(length(cons(z0, z1)), x1)) -> c12(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATLIST(cons(length(take(z0, z1)), x1)) -> c12(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__ISNAT(length(z0)))
   A__ISNATLIST(cons(x0, cons(x1, x2))) -> c13(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatList(x2))), A__ISNATLIST(cons(x1, x2)))
   A__ISNATLIST(cons(x0, cons(x1, nil))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNATLIST(cons(x1, nil)))
   A__ISNATLIST(cons(x0, cons(x1, cons(z0, z1)))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatList(z1)))), A__ISNATLIST(cons(x1, cons(z0, z1))))
   A__ISNATLIST(cons(x0, cons(x1, take(z0, z1)))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNATLIST(cons(x1, take(z0, z1))))
   A__ISNATLIST(cons(x0, cons(x1, z0))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatList(z0))), A__ISNATLIST(cons(x1, z0)))
   A__ISNATLIST(cons(x0, cons(0, x2))) -> c13(A__AND(a__isNat(x0), a__and(tt, a__isNatList(x2))), A__ISNATLIST(cons(0, x2)))
   A__ISNATLIST(cons(x0, cons(s(z0), x2))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(x2))), A__ISNATLIST(cons(s(z0), x2)))
   A__ISNATLIST(cons(x0, cons(length(z0), x2))) -> c13(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatList(x2))), A__ISNATLIST(cons(length(z0), x2)))
   A__ISNATLIST(cons(x0, cons(z0, x2))) -> c13(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatList(x2))), A__ISNATLIST(cons(z0, x2)))
   A__ISNATLIST(cons(0, cons(x1, x2))) -> c13(A__AND(tt, a__and(a__isNat(x1), a__isNatList(x2))), A__ISNATLIST(cons(x1, x2)))
   A__ISNATLIST(cons(s(z0), cons(x1, x2))) -> c13(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNATLIST(cons(x1, x2)))
   A__ISNATLIST(cons(length(z0), cons(x1, x2))) -> c13(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNATLIST(cons(x1, x2)))
   A__ISNATLIST(cons(z0, cons(x1, x2))) -> c13(A__ISNATLIST(cons(x1, x2)))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__UTAKE2_4, MARK_1, A__TAKE_2, A__ISNATLIST_1, A__LENGTH_1, A__ULENGTH_2

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c26_1, c35_1, c36_1, c37_1, c47_1, c48_1, c19_1, c42_1, c4_1, c5_1, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c15_1, c20_3, c20_2, c21_4, c21_3, c22_4, c22_3, c28_3, c28_2, c29_3, c29_2, c31_2, c29_1, c31_1, c33_2, c33_1, c34_2, c34_1, c38_2, c38_1, c40_2, c40_1, c41_2, c41_1, c43_2, c43_1, c44_2, c44_1, c4_2, c5_2, c12_2


----------------------------------------

(231) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__ISNATLIST(cons(x0, take(z0, z1))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATLIST(take(z0, z1))) by 
   A__ISNATLIST(cons(x0, take(x1, x2))) -> c13(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNATLIST(take(x1, x2)))
   A__ISNATLIST(cons(x0, take(x1, z0))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), A__ISNATLIST(take(x1, z0)))
   A__ISNATLIST(cons(x0, take(x1, zeros))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNATLIST(take(x1, zeros)))
   A__ISNATLIST(cons(x0, take(x1, cons(z0, z1)))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNATLIST(take(x1, cons(z0, z1))))
   A__ISNATLIST(cons(x0, take(x1, z0))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNATLIST(take(x1, z0)))
   A__ISNATLIST(cons(x0, take(0, x2))) -> c13(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNATLIST(take(0, x2)))
   A__ISNATLIST(cons(x0, take(s(z0), x2))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNATLIST(take(s(z0), x2)))
   A__ISNATLIST(cons(x0, take(length(z0), x2))) -> c13(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNATLIST(take(length(z0), x2)))
   A__ISNATLIST(cons(x0, take(z0, x2))) -> c13(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNATLIST(take(z0, x2)))
   A__ISNATLIST(cons(0, take(x1, x2))) -> c13(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATLIST(take(x1, x2)))
   A__ISNATLIST(cons(s(z0), take(x1, x2))) -> c13(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATLIST(take(x1, x2)))
   A__ISNATLIST(cons(length(z0), take(x1, x2))) -> c13(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATLIST(take(x1, x2)))
   A__ISNATLIST(cons(z0, take(x1, x2))) -> c13(A__AND(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATLIST(take(x1, x2)))

----------------------------------------

(232)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, isNatIList(x1)))
   A__ISNATILIST(cons(s(0), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(s(0)))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(nil), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(length(nil)))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__ISNAT(length(z0)))
   A__ISNATILIST(cons(x0, nil)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(nil))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(take(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(0, zeros)) -> c5(A__AND(tt, tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(s(z0), zeros)) -> c5(A__AND(a__isNat(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(length(z0), zeros)) -> c5(A__AND(a__isNatList(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNATILIST(cons(x1, zeros)))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNATILIST(cons(x1, cons(z0, z1))))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNATILIST(cons(x1, z0)))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c5(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNATILIST(cons(0, x2)))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(s(z0), x2)))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNATILIST(cons(length(z0), x2)))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c5(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(z0, x2)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c5(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c5(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c5(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(0), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(nil), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(s(z0), nil)) -> c12(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), nil)) -> c12(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, nil)) -> c12(A__AND(tt, tt))
   A__ISNATLIST(cons(z0, nil)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(x1, x2))) -> c12(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, nil))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, cons(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, take(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(0, x2))) -> c12(A__AND(a__isNat(x0), a__and(tt, a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(s(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(length(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, x2))) -> c12(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), cons(x1, x2))) -> c12(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), cons(x1, x2))) -> c12(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, cons(x1, x2))) -> c12(A__AND(tt, a__and(a__isNat(x1), a__isNatList(x2))))
   A__ISNATLIST(cons(z0, cons(x1, x2))) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, take(x1, x2))) -> c12(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, zeros))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, cons(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(0, x2))) -> c12(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(s(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(length(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, x2))) -> c12(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), take(x1, x2))) -> c12(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), take(x1, x2))) -> c12(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, take(x1, x2))) -> c12(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATLIST(cons(z0, take(x1, x2))) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, isNatList(x1)))
   A__ISNATLIST(cons(s(0), x1)) -> c12(A__AND(tt, a__isNatList(x1)), A__ISNAT(s(0)))
   A__ISNATLIST(cons(s(s(z0)), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATLIST(cons(s(length(z0)), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(nil), x1)) -> c12(A__AND(tt, a__isNatList(x1)), A__ISNAT(length(nil)))
   A__ISNATLIST(cons(length(cons(z0, z1)), x1)) -> c12(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATLIST(cons(length(take(z0, z1)), x1)) -> c12(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__ISNAT(length(z0)))
   A__ISNATLIST(cons(x0, cons(x1, x2))) -> c13(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatList(x2))), A__ISNATLIST(cons(x1, x2)))
   A__ISNATLIST(cons(x0, cons(x1, nil))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNATLIST(cons(x1, nil)))
   A__ISNATLIST(cons(x0, cons(x1, cons(z0, z1)))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatList(z1)))), A__ISNATLIST(cons(x1, cons(z0, z1))))
   A__ISNATLIST(cons(x0, cons(x1, take(z0, z1)))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNATLIST(cons(x1, take(z0, z1))))
   A__ISNATLIST(cons(x0, cons(x1, z0))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatList(z0))), A__ISNATLIST(cons(x1, z0)))
   A__ISNATLIST(cons(x0, cons(0, x2))) -> c13(A__AND(a__isNat(x0), a__and(tt, a__isNatList(x2))), A__ISNATLIST(cons(0, x2)))
   A__ISNATLIST(cons(x0, cons(s(z0), x2))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(x2))), A__ISNATLIST(cons(s(z0), x2)))
   A__ISNATLIST(cons(x0, cons(length(z0), x2))) -> c13(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatList(x2))), A__ISNATLIST(cons(length(z0), x2)))
   A__ISNATLIST(cons(x0, cons(z0, x2))) -> c13(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatList(x2))), A__ISNATLIST(cons(z0, x2)))
   A__ISNATLIST(cons(0, cons(x1, x2))) -> c13(A__AND(tt, a__and(a__isNat(x1), a__isNatList(x2))), A__ISNATLIST(cons(x1, x2)))
   A__ISNATLIST(cons(s(z0), cons(x1, x2))) -> c13(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNATLIST(cons(x1, x2)))
   A__ISNATLIST(cons(length(z0), cons(x1, x2))) -> c13(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNATLIST(cons(x1, x2)))
   A__ISNATLIST(cons(z0, cons(x1, x2))) -> c13(A__ISNATLIST(cons(x1, x2)))
   A__ISNATLIST(cons(x0, take(x1, x2))) -> c13(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNATLIST(take(x1, x2)))
   A__ISNATLIST(cons(x0, take(x1, z0))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), A__ISNATLIST(take(x1, z0)))
   A__ISNATLIST(cons(x0, take(x1, zeros))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNATLIST(take(x1, zeros)))
   A__ISNATLIST(cons(x0, take(x1, cons(z0, z1)))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNATLIST(take(x1, cons(z0, z1))))
   A__ISNATLIST(cons(x0, take(x1, z0))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNATLIST(take(x1, z0)))
   A__ISNATLIST(cons(x0, take(0, x2))) -> c13(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNATLIST(take(0, x2)))
   A__ISNATLIST(cons(x0, take(s(z0), x2))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNATLIST(take(s(z0), x2)))
   A__ISNATLIST(cons(x0, take(length(z0), x2))) -> c13(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNATLIST(take(length(z0), x2)))
   A__ISNATLIST(cons(x0, take(z0, x2))) -> c13(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNATLIST(take(z0, x2)))
   A__ISNATLIST(cons(0, take(x1, x2))) -> c13(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATLIST(take(x1, x2)))
   A__ISNATLIST(cons(s(z0), take(x1, x2))) -> c13(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATLIST(take(x1, x2)))
   A__ISNATLIST(cons(length(z0), take(x1, x2))) -> c13(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATLIST(take(x1, x2)))
   A__ISNATLIST(cons(z0, take(x1, x2))) -> c13(A__AND(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATLIST(take(x1, x2)))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, isNatIList(x1)))
   A__ISNATILIST(cons(s(0), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(s(0)))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(nil), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(length(nil)))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__ISNAT(length(z0)))
   A__ISNATILIST(cons(x0, nil)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(nil))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(take(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(0, zeros)) -> c5(A__AND(tt, tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(s(z0), zeros)) -> c5(A__AND(a__isNat(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(length(z0), zeros)) -> c5(A__AND(a__isNatList(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNATILIST(cons(x1, zeros)))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNATILIST(cons(x1, cons(z0, z1))))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNATILIST(cons(x1, z0)))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c5(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNATILIST(cons(0, x2)))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(s(z0), x2)))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNATILIST(cons(length(z0), x2)))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c5(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(z0, x2)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c5(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c5(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c5(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(0), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(nil), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(s(z0), nil)) -> c12(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), nil)) -> c12(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, nil)) -> c12(A__AND(tt, tt))
   A__ISNATLIST(cons(z0, nil)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(x1, x2))) -> c12(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, nil))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, cons(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, take(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(0, x2))) -> c12(A__AND(a__isNat(x0), a__and(tt, a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(s(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(length(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, x2))) -> c12(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), cons(x1, x2))) -> c12(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), cons(x1, x2))) -> c12(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, cons(x1, x2))) -> c12(A__AND(tt, a__and(a__isNat(x1), a__isNatList(x2))))
   A__ISNATLIST(cons(z0, cons(x1, x2))) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, take(x1, x2))) -> c12(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, zeros))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, cons(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(0, x2))) -> c12(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(s(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(length(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, x2))) -> c12(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), take(x1, x2))) -> c12(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), take(x1, x2))) -> c12(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, take(x1, x2))) -> c12(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATLIST(cons(z0, take(x1, x2))) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, isNatList(x1)))
   A__ISNATLIST(cons(s(0), x1)) -> c12(A__AND(tt, a__isNatList(x1)), A__ISNAT(s(0)))
   A__ISNATLIST(cons(s(s(z0)), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATLIST(cons(s(length(z0)), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(nil), x1)) -> c12(A__AND(tt, a__isNatList(x1)), A__ISNAT(length(nil)))
   A__ISNATLIST(cons(length(cons(z0, z1)), x1)) -> c12(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATLIST(cons(length(take(z0, z1)), x1)) -> c12(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__ISNAT(length(z0)))
   A__ISNATLIST(cons(x0, cons(x1, x2))) -> c13(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatList(x2))), A__ISNATLIST(cons(x1, x2)))
   A__ISNATLIST(cons(x0, cons(x1, nil))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNATLIST(cons(x1, nil)))
   A__ISNATLIST(cons(x0, cons(x1, cons(z0, z1)))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatList(z1)))), A__ISNATLIST(cons(x1, cons(z0, z1))))
   A__ISNATLIST(cons(x0, cons(x1, take(z0, z1)))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNATLIST(cons(x1, take(z0, z1))))
   A__ISNATLIST(cons(x0, cons(x1, z0))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatList(z0))), A__ISNATLIST(cons(x1, z0)))
   A__ISNATLIST(cons(x0, cons(0, x2))) -> c13(A__AND(a__isNat(x0), a__and(tt, a__isNatList(x2))), A__ISNATLIST(cons(0, x2)))
   A__ISNATLIST(cons(x0, cons(s(z0), x2))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(x2))), A__ISNATLIST(cons(s(z0), x2)))
   A__ISNATLIST(cons(x0, cons(length(z0), x2))) -> c13(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatList(x2))), A__ISNATLIST(cons(length(z0), x2)))
   A__ISNATLIST(cons(x0, cons(z0, x2))) -> c13(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatList(x2))), A__ISNATLIST(cons(z0, x2)))
   A__ISNATLIST(cons(0, cons(x1, x2))) -> c13(A__AND(tt, a__and(a__isNat(x1), a__isNatList(x2))), A__ISNATLIST(cons(x1, x2)))
   A__ISNATLIST(cons(s(z0), cons(x1, x2))) -> c13(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNATLIST(cons(x1, x2)))
   A__ISNATLIST(cons(length(z0), cons(x1, x2))) -> c13(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNATLIST(cons(x1, x2)))
   A__ISNATLIST(cons(z0, cons(x1, x2))) -> c13(A__ISNATLIST(cons(x1, x2)))
   A__ISNATLIST(cons(x0, take(x1, x2))) -> c13(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNATLIST(take(x1, x2)))
   A__ISNATLIST(cons(x0, take(x1, z0))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), A__ISNATLIST(take(x1, z0)))
   A__ISNATLIST(cons(x0, take(x1, zeros))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNATLIST(take(x1, zeros)))
   A__ISNATLIST(cons(x0, take(x1, cons(z0, z1)))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNATLIST(take(x1, cons(z0, z1))))
   A__ISNATLIST(cons(x0, take(x1, z0))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNATLIST(take(x1, z0)))
   A__ISNATLIST(cons(x0, take(0, x2))) -> c13(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNATLIST(take(0, x2)))
   A__ISNATLIST(cons(x0, take(s(z0), x2))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNATLIST(take(s(z0), x2)))
   A__ISNATLIST(cons(x0, take(length(z0), x2))) -> c13(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNATLIST(take(length(z0), x2)))
   A__ISNATLIST(cons(x0, take(z0, x2))) -> c13(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNATLIST(take(z0, x2)))
   A__ISNATLIST(cons(0, take(x1, x2))) -> c13(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATLIST(take(x1, x2)))
   A__ISNATLIST(cons(s(z0), take(x1, x2))) -> c13(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATLIST(take(x1, x2)))
   A__ISNATLIST(cons(length(z0), take(x1, x2))) -> c13(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATLIST(take(x1, x2)))
   A__ISNATLIST(cons(z0, take(x1, x2))) -> c13(A__AND(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATLIST(take(x1, x2)))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__UTAKE2_4, MARK_1, A__TAKE_2, A__ISNATLIST_1, A__LENGTH_1, A__ULENGTH_2

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c26_1, c35_1, c36_1, c37_1, c47_1, c48_1, c19_1, c42_1, c4_1, c5_1, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c15_1, c20_3, c20_2, c21_4, c21_3, c22_4, c22_3, c28_3, c28_2, c29_3, c29_2, c31_2, c29_1, c31_1, c33_2, c33_1, c34_2, c34_1, c38_2, c38_1, c40_2, c40_1, c41_2, c41_1, c43_2, c43_1, c44_2, c44_1, c4_2, c5_2, c12_2


----------------------------------------

(233) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing tuple parts
----------------------------------------

(234)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNatIList(z0) -> a__isNatList(z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNat(0) -> tt
   a__isNat(s(z0)) -> a__isNat(z0)
   a__isNat(length(z0)) -> a__isNatList(z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__and(a__isNat(z0), a__isNatList(z1))
   a__isNatList(take(z0, z1)) -> a__and(a__isNat(z0), a__isNatIList(z1))
   a__isNatList(z0) -> isNatList(z0)
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__take(0, z0) -> a__uTake1(a__isNatIList(z0))
   a__take(s(z0), cons(z1, z2)) -> a__uTake2(a__and(a__isNat(z0), a__and(a__isNat(z1), a__isNatIList(z2))), z0, z1, z2)
   a__take(z0, z1) -> take(z0, z1)
   a__uTake1(tt) -> nil
   a__uTake1(z0) -> uTake1(z0)
   a__uTake2(tt, z0, z1, z2) -> cons(mark(z1), take(z0, z2))
   a__uTake2(z0, z1, z2, z3) -> uTake2(z0, z1, z2, z3)
   a__length(cons(z0, z1)) -> a__uLength(a__and(a__isNat(z0), a__isNatList(z1)), z1)
   a__length(z0) -> length(z0)
   a__uLength(tt, z0) -> s(a__length(mark(z0)))
   a__uLength(z0, z1) -> uLength(z0, z1)
   mark(and(z0, z1)) -> a__and(mark(z0), mark(z1))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(isNat(z0)) -> a__isNat(z0)
   mark(length(z0)) -> a__length(mark(z0))
   mark(zeros) -> a__zeros
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(uTake1(z0)) -> a__uTake1(mark(z0))
   mark(uTake2(z0, z1, z2, z3)) -> a__uTake2(mark(z0), z1, z2, z3)
   mark(uLength(z0, z1)) -> a__uLength(mark(z0), z1)
   mark(tt) -> tt
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(nil) -> nil
Tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, isNatIList(x1)))
   A__ISNATILIST(cons(s(0), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(s(0)))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(nil), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(length(nil)))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__ISNAT(length(z0)))
   A__ISNATILIST(cons(x0, nil)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(nil))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(take(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(0, zeros)) -> c5(A__AND(tt, tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(s(z0), zeros)) -> c5(A__AND(a__isNat(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(length(z0), zeros)) -> c5(A__AND(a__isNatList(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNATILIST(cons(x1, zeros)))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNATILIST(cons(x1, cons(z0, z1))))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNATILIST(cons(x1, z0)))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c5(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNATILIST(cons(0, x2)))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(s(z0), x2)))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNATILIST(cons(length(z0), x2)))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c5(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(z0, x2)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c5(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c5(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c5(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(0), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(nil), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(s(z0), nil)) -> c12(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), nil)) -> c12(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, nil)) -> c12(A__AND(tt, tt))
   A__ISNATLIST(cons(z0, nil)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(x1, x2))) -> c12(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, nil))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, cons(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, take(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(0, x2))) -> c12(A__AND(a__isNat(x0), a__and(tt, a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(s(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(length(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, x2))) -> c12(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), cons(x1, x2))) -> c12(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), cons(x1, x2))) -> c12(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, cons(x1, x2))) -> c12(A__AND(tt, a__and(a__isNat(x1), a__isNatList(x2))))
   A__ISNATLIST(cons(z0, cons(x1, x2))) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, take(x1, x2))) -> c12(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, zeros))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, cons(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(0, x2))) -> c12(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(s(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(length(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, x2))) -> c12(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), take(x1, x2))) -> c12(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), take(x1, x2))) -> c12(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, take(x1, x2))) -> c12(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATLIST(cons(z0, take(x1, x2))) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, isNatList(x1)))
   A__ISNATLIST(cons(s(0), x1)) -> c12(A__AND(tt, a__isNatList(x1)), A__ISNAT(s(0)))
   A__ISNATLIST(cons(s(s(z0)), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATLIST(cons(s(length(z0)), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(nil), x1)) -> c12(A__AND(tt, a__isNatList(x1)), A__ISNAT(length(nil)))
   A__ISNATLIST(cons(length(cons(z0, z1)), x1)) -> c12(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATLIST(cons(length(take(z0, z1)), x1)) -> c12(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__ISNAT(length(z0)))
   A__ISNATLIST(cons(x0, cons(x1, x2))) -> c13(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatList(x2))), A__ISNATLIST(cons(x1, x2)))
   A__ISNATLIST(cons(x0, cons(x1, nil))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNATLIST(cons(x1, nil)))
   A__ISNATLIST(cons(x0, cons(x1, cons(z0, z1)))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatList(z1)))), A__ISNATLIST(cons(x1, cons(z0, z1))))
   A__ISNATLIST(cons(x0, cons(x1, take(z0, z1)))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNATLIST(cons(x1, take(z0, z1))))
   A__ISNATLIST(cons(x0, cons(x1, z0))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatList(z0))), A__ISNATLIST(cons(x1, z0)))
   A__ISNATLIST(cons(x0, cons(0, x2))) -> c13(A__AND(a__isNat(x0), a__and(tt, a__isNatList(x2))), A__ISNATLIST(cons(0, x2)))
   A__ISNATLIST(cons(x0, cons(s(z0), x2))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(x2))), A__ISNATLIST(cons(s(z0), x2)))
   A__ISNATLIST(cons(x0, cons(length(z0), x2))) -> c13(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatList(x2))), A__ISNATLIST(cons(length(z0), x2)))
   A__ISNATLIST(cons(x0, cons(z0, x2))) -> c13(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatList(x2))), A__ISNATLIST(cons(z0, x2)))
   A__ISNATLIST(cons(0, cons(x1, x2))) -> c13(A__AND(tt, a__and(a__isNat(x1), a__isNatList(x2))), A__ISNATLIST(cons(x1, x2)))
   A__ISNATLIST(cons(s(z0), cons(x1, x2))) -> c13(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNATLIST(cons(x1, x2)))
   A__ISNATLIST(cons(length(z0), cons(x1, x2))) -> c13(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNATLIST(cons(x1, x2)))
   A__ISNATLIST(cons(z0, cons(x1, x2))) -> c13(A__ISNATLIST(cons(x1, x2)))
   A__ISNATLIST(cons(x0, take(x1, x2))) -> c13(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNATLIST(take(x1, x2)))
   A__ISNATLIST(cons(x0, take(x1, z0))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), A__ISNATLIST(take(x1, z0)))
   A__ISNATLIST(cons(x0, take(x1, zeros))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNATLIST(take(x1, zeros)))
   A__ISNATLIST(cons(x0, take(x1, cons(z0, z1)))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNATLIST(take(x1, cons(z0, z1))))
   A__ISNATLIST(cons(x0, take(x1, z0))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNATLIST(take(x1, z0)))
   A__ISNATLIST(cons(x0, take(0, x2))) -> c13(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNATLIST(take(0, x2)))
   A__ISNATLIST(cons(x0, take(s(z0), x2))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNATLIST(take(s(z0), x2)))
   A__ISNATLIST(cons(x0, take(length(z0), x2))) -> c13(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNATLIST(take(length(z0), x2)))
   A__ISNATLIST(cons(x0, take(z0, x2))) -> c13(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNATLIST(take(z0, x2)))
   A__ISNATLIST(cons(0, take(x1, x2))) -> c13(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATLIST(take(x1, x2)))
   A__ISNATLIST(cons(s(z0), take(x1, x2))) -> c13(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATLIST(take(x1, x2)))
   A__ISNATLIST(cons(length(z0), take(x1, x2))) -> c13(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATLIST(take(x1, x2)))
   A__ISNATLIST(cons(z0, take(x1, x2))) -> c13(A__ISNATLIST(take(x1, x2)))
S tuples:
   A__AND(tt, z0) -> c(MARK(z0))
   A__ISNATILIST(z0) -> c2(A__ISNATLIST(z0))
   A__ISNAT(s(z0)) -> c8(A__ISNAT(z0))
   A__ISNAT(length(z0)) -> c9(A__ISNATLIST(z0))
   A__UTAKE2(tt, z0, z1, z2) -> c26(MARK(z1))
   MARK(isNatIList(z0)) -> c35(A__ISNATILIST(z0))
   MARK(isNatList(z0)) -> c36(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c37(A__ISNAT(z0))
   MARK(s(z0)) -> c47(MARK(z0))
   MARK(cons(z0, z1)) -> c48(MARK(z0))
   A__TAKE(0, z0) -> c19(A__ISNATILIST(z0))
   MARK(uTake1(z0)) -> c42(MARK(z0))
   A__ISNATILIST(cons(z0, x1)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(z0, x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(z0, x1)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, z0)) -> c13(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATLIST(z0))
   A__ISNATLIST(cons(0, x1)) -> c13(A__AND(tt, a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(s(z0), x1)) -> c13(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(length(z0), x1)) -> c13(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ISNATLIST(cons(x0, nil)) -> c13(A__AND(a__isNat(x0), tt))
   A__ISNATLIST(cons(z0, x1)) -> c13(A__ISNATLIST(x1))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(x0, zeros)) -> c14(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c14(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATLIST(take(x0, z0)) -> c14(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNAT(x0))
   A__ISNATLIST(take(s(z0), x1)) -> c14(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(take(length(z0), x1)) -> c14(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(take(0, x1)) -> c14(A__AND(tt, a__isNatIList(x1)))
   A__ISNATLIST(take(z0, x1)) -> c14(A__ISNAT(z0))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(x0, zeros)) -> c15(A__AND(a__isNat(x0), tt), A__ISNATILIST(zeros))
   A__ISNATLIST(take(x0, cons(z0, z1))) -> c15(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATLIST(take(x0, z0)) -> c15(A__AND(a__isNat(x0), isNatIList(z0)), A__ISNATILIST(z0))
   A__ISNATLIST(take(0, x1)) -> c15(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(s(z0), x1)) -> c15(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(length(z0), x1)) -> c15(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATLIST(take(z0, x1)) -> c15(A__ISNATILIST(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(x1, z0)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(x0), cons(z0, x2)) -> c20(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c20(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__TAKE(s(z0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c20(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__TAKE(s(0), cons(x1, x2)) -> c20(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, zeros)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, z0)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNAT(s(z0)))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNAT(length(z0)))
   A__TAKE(s(x0), cons(z0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNAT(z0))
   A__TAKE(s(0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c21(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(z0), cons(x1, x2)) -> c21(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(x1, x2)) -> c21(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNAT(x1))
   A__TAKE(s(x0), cons(0, x2)) -> c21(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), x0, x1, x2), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), tt)), x0, x1, zeros), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(zeros))), A__AND(a__isNat(x1), a__isNatIList(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), x0, x1, cons(z0, z1)), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(cons(z0, z1)))), A__AND(a__isNat(x1), a__isNatIList(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), x0, x1, z0), A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(z0))), A__AND(a__isNat(x1), a__isNatIList(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(tt, a__isNatIList(x2))), x0, 0, x2), A__AND(a__isNat(x0), a__and(a__isNat(0), a__isNatIList(x2))), A__AND(a__isNat(0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(s(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), x0, s(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(s(z0)), a__isNatIList(x2))), A__AND(a__isNat(s(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(length(z0), x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), x0, length(z0), x2), A__AND(a__isNat(x0), a__and(a__isNat(length(z0)), a__isNatIList(x2))), A__AND(a__isNat(length(z0)), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(z0, x2)) -> c22(A__UTAKE2(a__and(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), x0, z0, x2), A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__AND(a__isNat(z0), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(tt, a__and(a__isNat(x1), a__isNatIList(x2))), 0, x1, x2), A__AND(a__isNat(0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(s(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), s(z0), x1, x2), A__AND(a__isNat(s(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(length(z0)), cons(x1, x2)) -> c22(A__UTAKE2(a__and(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), length(z0), x1, x2), A__AND(a__isNat(length(z0)), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(z0), cons(x1, x2)) -> c22(A__UTAKE2(a__and(isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), z0, x1, x2), A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c22(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatIList(x2))), A__AND(a__isNat(x1), a__isNatIList(x2)), A__ISNATILIST(x2))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, take(z0, z1))) -> c28(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNAT(x0))
   A__LENGTH(cons(x0, z0)) -> c28(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNAT(x0))
   A__LENGTH(cons(s(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__LENGTH(cons(length(z0), x1)) -> c28(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__LENGTH(cons(z0, x1)) -> c28(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(z0))
   A__LENGTH(cons(x0, x1)) -> c28(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNAT(x0))
   A__LENGTH(cons(0, x1)) -> c28(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), cons(z0, z1)), A__AND(a__isNat(x0), a__isNatList(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c29(A__ULENGTH(a__and(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), take(z0, z1)), A__AND(a__isNat(x0), a__isNatList(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c29(A__ULENGTH(a__and(a__isNat(x0), isNatList(z0)), z0), A__AND(a__isNat(x0), a__isNatList(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(0, x1)) -> c29(A__ULENGTH(a__and(tt, a__isNatList(x1)), x1), A__AND(a__isNat(0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(s(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(s(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(length(z0), x1)) -> c29(A__ULENGTH(a__and(a__isNatList(z0), a__isNatList(x1)), x1), A__AND(a__isNat(length(z0)), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(z0, x1)) -> c29(A__ULENGTH(a__and(isNat(z0), a__isNatList(x1)), x1), A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c29(A__AND(a__isNat(x0), a__isNatList(x1)), A__ISNATLIST(x1))
   A__ULENGTH(tt, and(z0, z1)) -> c31(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   A__ULENGTH(tt, isNatIList(z0)) -> c31(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__ULENGTH(tt, isNatList(z0)) -> c31(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__ULENGTH(tt, isNat(z0)) -> c31(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__ULENGTH(tt, length(z0)) -> c31(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__ULENGTH(tt, take(z0, z1)) -> c31(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__ULENGTH(tt, uTake1(z0)) -> c31(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   A__ULENGTH(tt, uTake2(z0, z1, z2, z3)) -> c31(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   A__ULENGTH(tt, uLength(z0, z1)) -> c31(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   A__ULENGTH(tt, cons(z0, z1)) -> c31(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__LENGTH(cons(x0, nil)) -> c28(A__AND(a__isNat(x0), a__isNatList(nil)), A__ISNAT(x0))
   A__LENGTH(cons(x0, nil)) -> c29(A__AND(a__isNat(x0), a__isNatList(nil)))
   A__ULENGTH(tt, zeros) -> c31(A__LENGTH(a__zeros))
   A__ULENGTH(tt, s(z0)) -> c31(MARK(s(z0)))
   MARK(and(x0, and(z0, z1))) -> c33(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, isNatIList(z0))) -> c33(A__AND(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(and(x0, isNatList(z0))) -> c33(A__AND(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(and(x0, isNat(z0))) -> c33(A__AND(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(and(x0, length(z0))) -> c33(A__AND(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(and(x0, zeros)) -> c33(A__AND(mark(x0), a__zeros), MARK(x0))
   MARK(and(x0, take(z0, z1))) -> c33(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(and(x0, uTake1(z0))) -> c33(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c33(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(and(x0, uLength(z0, z1))) -> c33(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(and(x0, tt)) -> c33(A__AND(mark(x0), tt), MARK(x0))
   MARK(and(x0, 0)) -> c33(A__AND(mark(x0), 0), MARK(x0))
   MARK(and(x0, s(z0))) -> c33(A__AND(mark(x0), s(mark(z0))), MARK(x0))
   MARK(and(x0, cons(z0, z1))) -> c33(A__AND(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(and(x0, nil)) -> c33(A__AND(mark(x0), nil), MARK(x0))
   MARK(and(and(z0, z1), x1)) -> c33(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(and(isNatIList(z0), x1)) -> c33(A__AND(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(and(isNatList(z0), x1)) -> c33(A__AND(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(and(isNat(z0), x1)) -> c33(A__AND(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(and(length(z0), x1)) -> c33(A__AND(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(and(take(z0, z1), x1)) -> c33(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(and(uTake1(z0), x1)) -> c33(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c33(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(uLength(z0, z1), x1)) -> c33(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(and(zeros, x1)) -> c33(A__AND(a__zeros, mark(x1)))
   MARK(and(tt, x1)) -> c33(A__AND(tt, mark(x1)))
   MARK(and(s(z0), x1)) -> c33(MARK(s(z0)))
   MARK(and(cons(z0, z1), x1)) -> c33(MARK(cons(z0, z1)))
   MARK(and(x0, and(z0, z1))) -> c34(A__AND(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(and(x0, isNatIList(z0))) -> c34(A__AND(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(and(x0, isNatList(z0))) -> c34(A__AND(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(and(x0, isNat(z0))) -> c34(A__AND(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(and(x0, length(z0))) -> c34(A__AND(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(and(x0, take(z0, z1))) -> c34(A__AND(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(and(x0, uTake1(z0))) -> c34(A__AND(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(and(x0, uTake2(z0, z1, z2, z3))) -> c34(A__AND(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(and(x0, uLength(z0, z1))) -> c34(A__AND(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(and(x0, s(z0))) -> c34(A__AND(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(and(x0, cons(z0, z1))) -> c34(A__AND(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c34(A__AND(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(isNatIList(z0), x1)) -> c34(A__AND(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(and(isNatList(z0), x1)) -> c34(A__AND(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(and(isNat(z0), x1)) -> c34(A__AND(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(and(length(z0), x1)) -> c34(A__AND(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(zeros, x1)) -> c34(A__AND(a__zeros, mark(x1)), MARK(x1))
   MARK(and(take(z0, z1), x1)) -> c34(A__AND(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(and(uTake1(z0), x1)) -> c34(A__AND(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(and(uTake2(z0, z1, z2, z3), x1)) -> c34(A__AND(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(and(uLength(z0, z1), x1)) -> c34(A__AND(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(and(tt, x1)) -> c34(A__AND(tt, mark(x1)), MARK(x1))
   MARK(and(x0, zeros)) -> c34(A__AND(mark(x0), a__zeros))
   MARK(and(x0, tt)) -> c34(A__AND(mark(x0), tt))
   MARK(and(x0, 0)) -> c34(A__AND(mark(x0), 0))
   MARK(and(x0, nil)) -> c34(A__AND(mark(x0), nil))
   MARK(and(0, x1)) -> c34(MARK(x1))
   MARK(and(s(z0), x1)) -> c34(MARK(x1))
   MARK(and(cons(z0, z1), x1)) -> c34(MARK(x1))
   MARK(and(nil, x1)) -> c34(MARK(x1))
   MARK(length(and(z0, z1))) -> c38(A__LENGTH(a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(length(isNatIList(z0))) -> c38(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(isNatList(z0))) -> c38(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(isNat(z0))) -> c38(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(length(z0))) -> c38(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(take(z0, z1))) -> c38(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(uTake1(z0))) -> c38(A__LENGTH(a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(length(uTake2(z0, z1, z2, z3))) -> c38(A__LENGTH(a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(length(uLength(z0, z1))) -> c38(A__LENGTH(a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(length(cons(z0, z1))) -> c38(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c38(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c38(MARK(s(z0)))
   MARK(take(x0, and(z0, z1))) -> c40(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c40(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c40(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c40(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, length(z0))) -> c40(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, zeros)) -> c40(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c40(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, uTake1(z0))) -> c40(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(x0))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c40(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, uLength(z0, z1))) -> c40(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(x0))
   MARK(take(x0, tt)) -> c40(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, 0)) -> c40(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, s(z0))) -> c40(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c40(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, nil)) -> c40(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(and(z0, z1), x1)) -> c40(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIList(z0), x1)) -> c40(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(isNatList(z0), x1)) -> c40(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(isNat(z0), x1)) -> c40(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(length(z0), x1)) -> c40(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(take(z0, z1), x1)) -> c40(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(uTake1(z0), x1)) -> c40(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(uTake1(z0)))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c40(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(uLength(z0, z1), x1)) -> c40(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(uLength(z0, z1)))
   MARK(take(s(z0), x1)) -> c40(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c40(A__TAKE(a__zeros, mark(x1)))
   MARK(take(0, x1)) -> c40(A__TAKE(0, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c40(MARK(cons(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c41(A__TAKE(mark(x0), a__and(mark(z0), mark(z1))), MARK(and(z0, z1)))
   MARK(take(x0, isNatIList(z0))) -> c41(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, isNatList(z0))) -> c41(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, isNat(z0))) -> c41(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, length(z0))) -> c41(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, take(z0, z1))) -> c41(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, uTake1(z0))) -> c41(A__TAKE(mark(x0), a__uTake1(mark(z0))), MARK(uTake1(z0)))
   MARK(take(x0, uTake2(z0, z1, z2, z3))) -> c41(A__TAKE(mark(x0), a__uTake2(mark(z0), z1, z2, z3)), MARK(uTake2(z0, z1, z2, z3)))
   MARK(take(x0, uLength(z0, z1))) -> c41(A__TAKE(mark(x0), a__uLength(mark(z0), z1)), MARK(uLength(z0, z1)))
   MARK(take(x0, s(z0))) -> c41(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, cons(z0, z1))) -> c41(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c41(A__TAKE(a__and(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c41(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c41(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c41(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c41(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(zeros, x1)) -> c41(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c41(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(uTake1(z0), x1)) -> c41(A__TAKE(a__uTake1(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(uTake2(z0, z1, z2, z3), x1)) -> c41(A__TAKE(a__uTake2(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(uLength(z0, z1), x1)) -> c41(A__TAKE(a__uLength(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c41(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c41(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c41(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, tt)) -> c41(A__TAKE(mark(x0), tt))
   MARK(take(x0, 0)) -> c41(A__TAKE(mark(x0), 0))
   MARK(take(x0, nil)) -> c41(A__TAKE(mark(x0), nil))
   MARK(take(tt, x1)) -> c41(MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c41(MARK(x1))
   MARK(take(nil, x1)) -> c41(MARK(x1))
   MARK(uTake2(and(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__and(mark(z0), mark(z1)), x1, x2, x3), MARK(and(z0, z1)))
   MARK(uTake2(isNatIList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(uTake2(isNatList(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(uTake2(isNat(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(uTake2(length(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(uTake2(take(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(uTake2(uTake1(z0), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake1(mark(z0)), x1, x2, x3), MARK(uTake1(z0)))
   MARK(uTake2(uTake2(z0, z1, z2, z3), x1, x2, x3)) -> c43(A__UTAKE2(a__uTake2(mark(z0), z1, z2, z3), x1, x2, x3), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uTake2(uLength(z0, z1), x1, x2, x3)) -> c43(A__UTAKE2(a__uLength(mark(z0), z1), x1, x2, x3), MARK(uLength(z0, z1)))
   MARK(uTake2(zeros, x1, x2, x3)) -> c43(A__UTAKE2(a__zeros, x1, x2, x3))
   MARK(uTake2(tt, x1, x2, x3)) -> c43(A__UTAKE2(tt, x1, x2, x3))
   MARK(uTake2(s(z0), x1, x2, x3)) -> c43(MARK(s(z0)))
   MARK(uTake2(cons(z0, z1), x1, x2, x3)) -> c43(MARK(cons(z0, z1)))
   MARK(uLength(and(z0, z1), x1)) -> c44(A__ULENGTH(a__and(mark(z0), mark(z1)), x1), MARK(and(z0, z1)))
   MARK(uLength(isNatIList(z0), x1)) -> c44(A__ULENGTH(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(uLength(isNatList(z0), x1)) -> c44(A__ULENGTH(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(uLength(isNat(z0), x1)) -> c44(A__ULENGTH(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(uLength(length(z0), x1)) -> c44(A__ULENGTH(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(uLength(take(z0, z1), x1)) -> c44(A__ULENGTH(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(uLength(uTake1(z0), x1)) -> c44(A__ULENGTH(a__uTake1(mark(z0)), x1), MARK(uTake1(z0)))
   MARK(uLength(uTake2(z0, z1, z2, z3), x1)) -> c44(A__ULENGTH(a__uTake2(mark(z0), z1, z2, z3), x1), MARK(uTake2(z0, z1, z2, z3)))
   MARK(uLength(uLength(z0, z1), x1)) -> c44(A__ULENGTH(a__uLength(mark(z0), z1), x1), MARK(uLength(z0, z1)))
   MARK(uLength(zeros, x1)) -> c44(A__ULENGTH(a__zeros, x1))
   MARK(uLength(tt, x1)) -> c44(A__ULENGTH(tt, x1))
   MARK(uLength(s(z0), x1)) -> c44(MARK(s(z0)))
   MARK(uLength(cons(z0, z1), x1)) -> c44(MARK(cons(z0, z1)))
   A__ISNATILIST(cons(x0, nil)) -> c4(A__AND(a__isNat(x0), tt), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, z0)) -> c4(A__AND(a__isNat(x0), isNatList(z0)), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, a__isNatList(x1)))
   A__ISNATILIST(cons(s(z0), zeros)) -> c4(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), zeros)) -> c4(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, zeros)) -> c4(A__AND(tt, tt))
   A__ISNATILIST(cons(z0, zeros)) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c4(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c4(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c4(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c4(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c4(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c4(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c4(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATILIST(cons(z0, cons(x1, x2))) -> c4(A__ISNAT(z0))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNAT(length(z0)))
   A__ISNATILIST(cons(0, x1)) -> c4(A__AND(tt, isNatIList(x1)))
   A__ISNATILIST(cons(s(0), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(s(0)))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c4(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c4(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATILIST(cons(s(z0), x1)) -> c4(A__ISNAT(s(z0)))
   A__ISNATILIST(cons(length(nil), x1)) -> c4(A__AND(tt, a__isNatIList(x1)), A__ISNAT(length(nil)))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c4(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATILIST(cons(length(z0), x1)) -> c4(A__ISNAT(length(z0)))
   A__ISNATILIST(cons(x0, nil)) -> c5(A__AND(a__isNat(x0), tt), A__ISNATILIST(nil))
   A__ISNATILIST(cons(x0, cons(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(z1))), A__ISNATILIST(cons(z0, z1)))
   A__ISNATILIST(cons(x0, take(z0, z1))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(z1))), A__ISNATILIST(take(z0, z1)))
   A__ISNATILIST(cons(x0, z0)) -> c5(A__AND(a__isNat(x0), isNatList(z0)), A__ISNATILIST(z0))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(0, zeros)) -> c5(A__AND(tt, tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(s(z0), zeros)) -> c5(A__AND(a__isNat(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(length(z0), zeros)) -> c5(A__AND(a__isNatList(z0), tt), A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, zeros)) -> c5(A__ISNATILIST(zeros))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, zeros))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNATILIST(cons(x1, zeros)))
   A__ISNATILIST(cons(x0, cons(x1, cons(z0, z1)))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNATILIST(cons(x1, cons(z0, z1))))
   A__ISNATILIST(cons(x0, cons(x1, z0))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNATILIST(cons(x1, z0)))
   A__ISNATILIST(cons(x0, cons(0, x2))) -> c5(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNATILIST(cons(0, x2)))
   A__ISNATILIST(cons(x0, cons(s(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(s(z0), x2)))
   A__ISNATILIST(cons(x0, cons(length(z0), x2))) -> c5(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNATILIST(cons(length(z0), x2)))
   A__ISNATILIST(cons(x0, cons(z0, x2))) -> c5(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNATILIST(cons(z0, x2)))
   A__ISNATILIST(cons(0, cons(x1, x2))) -> c5(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(s(z0), cons(x1, x2))) -> c5(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(length(z0), cons(x1, x2))) -> c5(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(x0, cons(x1, x2))) -> c5(A__ISNATILIST(cons(x1, x2)))
   A__ISNATILIST(cons(0, x1)) -> c5(A__AND(tt, isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__AND(a__isNat(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__AND(a__isNatList(z0), isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(0), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(s(z0)), x1)) -> c5(A__AND(a__isNat(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(length(z0)), x1)) -> c5(A__AND(a__isNatList(z0), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(s(z0), x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(nil), x1)) -> c5(A__AND(tt, a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(cons(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(take(z0, z1)), x1)) -> c5(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatIList(x1)), A__ISNATILIST(x1))
   A__ISNATILIST(cons(length(z0), x1)) -> c5(A__ISNATILIST(x1))
   A__ISNATLIST(cons(s(z0), nil)) -> c12(A__AND(a__isNat(z0), tt), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), nil)) -> c12(A__AND(a__isNatList(z0), tt), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, nil)) -> c12(A__AND(tt, tt))
   A__ISNATLIST(cons(z0, nil)) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, cons(x1, x2))) -> c12(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, nil))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, cons(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, take(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(0, x2))) -> c12(A__AND(a__isNat(x0), a__and(tt, a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(s(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(length(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, cons(z0, x2))) -> c12(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), cons(x1, x2))) -> c12(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), cons(x1, x2))) -> c12(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, cons(x1, x2))) -> c12(A__AND(tt, a__and(a__isNat(x1), a__isNatList(x2))))
   A__ISNATLIST(cons(z0, cons(x1, x2))) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(x0, take(x1, x2))) -> c12(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, zeros))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, cons(z0, z1)))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(x1, z0))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(0, x2))) -> c12(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(s(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(length(z0), x2))) -> c12(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(x0, take(z0, x2))) -> c12(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNAT(x0))
   A__ISNATLIST(cons(s(z0), take(x1, x2))) -> c12(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), take(x1, x2))) -> c12(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, take(x1, x2))) -> c12(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))))
   A__ISNATLIST(cons(z0, take(x1, x2))) -> c12(A__ISNAT(z0))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__AND(a__isNat(z0), isNatList(x1)), A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__AND(a__isNatList(z0), isNatList(x1)), A__ISNAT(length(z0)))
   A__ISNATLIST(cons(0, x1)) -> c12(A__AND(tt, isNatList(x1)))
   A__ISNATLIST(cons(s(0), x1)) -> c12(A__AND(tt, a__isNatList(x1)), A__ISNAT(s(0)))
   A__ISNATLIST(cons(s(s(z0)), x1)) -> c12(A__AND(a__isNat(z0), a__isNatList(x1)), A__ISNAT(s(s(z0))))
   A__ISNATLIST(cons(s(length(z0)), x1)) -> c12(A__AND(a__isNatList(z0), a__isNatList(x1)), A__ISNAT(s(length(z0))))
   A__ISNATLIST(cons(s(z0), x1)) -> c12(A__ISNAT(s(z0)))
   A__ISNATLIST(cons(length(nil), x1)) -> c12(A__AND(tt, a__isNatList(x1)), A__ISNAT(length(nil)))
   A__ISNATLIST(cons(length(cons(z0, z1)), x1)) -> c12(A__AND(a__and(a__isNat(z0), a__isNatList(z1)), a__isNatList(x1)), A__ISNAT(length(cons(z0, z1))))
   A__ISNATLIST(cons(length(take(z0, z1)), x1)) -> c12(A__AND(a__and(a__isNat(z0), a__isNatIList(z1)), a__isNatList(x1)), A__ISNAT(length(take(z0, z1))))
   A__ISNATLIST(cons(length(z0), x1)) -> c12(A__ISNAT(length(z0)))
   A__ISNATLIST(cons(x0, cons(x1, x2))) -> c13(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatList(x2))), A__ISNATLIST(cons(x1, x2)))
   A__ISNATLIST(cons(x0, cons(x1, nil))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNATLIST(cons(x1, nil)))
   A__ISNATLIST(cons(x0, cons(x1, cons(z0, z1)))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatList(z1)))), A__ISNATLIST(cons(x1, cons(z0, z1))))
   A__ISNATLIST(cons(x0, cons(x1, take(z0, z1)))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNATLIST(cons(x1, take(z0, z1))))
   A__ISNATLIST(cons(x0, cons(x1, z0))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatList(z0))), A__ISNATLIST(cons(x1, z0)))
   A__ISNATLIST(cons(x0, cons(0, x2))) -> c13(A__AND(a__isNat(x0), a__and(tt, a__isNatList(x2))), A__ISNATLIST(cons(0, x2)))
   A__ISNATLIST(cons(x0, cons(s(z0), x2))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatList(x2))), A__ISNATLIST(cons(s(z0), x2)))
   A__ISNATLIST(cons(x0, cons(length(z0), x2))) -> c13(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatList(x2))), A__ISNATLIST(cons(length(z0), x2)))
   A__ISNATLIST(cons(x0, cons(z0, x2))) -> c13(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatList(x2))), A__ISNATLIST(cons(z0, x2)))
   A__ISNATLIST(cons(0, cons(x1, x2))) -> c13(A__AND(tt, a__and(a__isNat(x1), a__isNatList(x2))), A__ISNATLIST(cons(x1, x2)))
   A__ISNATLIST(cons(s(z0), cons(x1, x2))) -> c13(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNATLIST(cons(x1, x2)))
   A__ISNATLIST(cons(length(z0), cons(x1, x2))) -> c13(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatList(x2))), A__ISNATLIST(cons(x1, x2)))
   A__ISNATLIST(cons(z0, cons(x1, x2))) -> c13(A__ISNATLIST(cons(x1, x2)))
   A__ISNATLIST(cons(x0, take(x1, x2))) -> c13(A__AND(a__isNat(x0), and(a__isNat(x1), a__isNatIList(x2))), A__ISNATLIST(take(x1, x2)))
   A__ISNATLIST(cons(x0, take(x1, z0))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__isNatList(z0))), A__ISNATLIST(take(x1, z0)))
   A__ISNATLIST(cons(x0, take(x1, zeros))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(x1), tt)), A__ISNATLIST(take(x1, zeros)))
   A__ISNATLIST(cons(x0, take(x1, cons(z0, z1)))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(x1), a__and(a__isNat(z0), a__isNatIList(z1)))), A__ISNATLIST(take(x1, cons(z0, z1))))
   A__ISNATLIST(cons(x0, take(x1, z0))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(x1), isNatIList(z0))), A__ISNATLIST(take(x1, z0)))
   A__ISNATLIST(cons(x0, take(0, x2))) -> c13(A__AND(a__isNat(x0), a__and(tt, a__isNatIList(x2))), A__ISNATLIST(take(0, x2)))
   A__ISNATLIST(cons(x0, take(s(z0), x2))) -> c13(A__AND(a__isNat(x0), a__and(a__isNat(z0), a__isNatIList(x2))), A__ISNATLIST(take(s(z0), x2)))
   A__ISNATLIST(cons(x0, take(length(z0), x2))) -> c13(A__AND(a__isNat(x0), a__and(a__isNatList(z0), a__isNatIList(x2))), A__ISNATLIST(take(length(z0), x2)))
   A__ISNATLIST(cons(x0, take(z0, x2))) -> c13(A__AND(a__isNat(x0), a__and(isNat(z0), a__isNatIList(x2))), A__ISNATLIST(take(z0, x2)))
   A__ISNATLIST(cons(0, take(x1, x2))) -> c13(A__AND(tt, a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATLIST(take(x1, x2)))
   A__ISNATLIST(cons(s(z0), take(x1, x2))) -> c13(A__AND(a__isNat(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATLIST(take(x1, x2)))
   A__ISNATLIST(cons(length(z0), take(x1, x2))) -> c13(A__AND(a__isNatList(z0), a__and(a__isNat(x1), a__isNatIList(x2))), A__ISNATLIST(take(x1, x2)))
   A__ISNATLIST(cons(z0, take(x1, x2))) -> c13(A__ISNATLIST(take(x1, x2)))
K tuples:none
Defined Rule Symbols:   a__and_2, a__isNatIList_1, a__isNat_1, a__isNatList_1, a__zeros, a__take_2, a__uTake1_1, a__uTake2_4, a__length_1, a__uLength_2, mark_1

Defined Pair Symbols:   A__AND_2, A__ISNATILIST_1, A__ISNAT_1, A__UTAKE2_4, MARK_1, A__TAKE_2, A__ISNATLIST_1, A__LENGTH_1, A__ULENGTH_2

Compound Symbols:   c_1, c2_1, c8_1, c9_1, c26_1, c35_1, c36_1, c37_1, c47_1, c48_1, c19_1, c42_1, c4_1, c5_1, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c15_1, c20_3, c20_2, c21_4, c21_3, c22_4, c22_3, c28_3, c28_2, c29_3, c29_2, c31_2, c29_1, c31_1, c33_2, c33_1, c34_2, c34_1, c38_2, c38_1, c40_2, c40_1, c41_2, c41_1, c43_2, c43_1, c44_2, c44_1, c4_2, c5_2, c12_2